In a Word, Yes
Yes, in Greek mythology, deities would fairly often assume the forms of other deities. The instances are certainly not as numerous as the stories in which the gods take on the shapes of humans, beasts or other non-divine objects, and they (examples of a certain god appearing as another one, i.e.) almost all occur in Nonnus' Dionysiaka [Dionysiaca].
And yes, there are some instances in which the stories clearly do limit the ability in some way. There is no story in which the form assumed somehow grants its bearer the same powers or capabilities as the individual s\he is impersonating, at least not beyond him/her projecting the mere façade of possessing those powers, which is, after all, in line with the whole point thereof.
And indeed, for Nonnus, the primary (and, in most cases, exclusive) function of this sort of metamorphosis is impersonation. As is the case in other mythographers, the metamorphoses are always in pursuit of short-term goals, whether the deity in view happens to be impersonating another deity or a mortal entity.
The mechanics thereof are never described in enough detail for a definitive conclusion to be reached on this aspect of the issue, but a few stories imply that the transformations are essentially impermanent, whether it is because the impersonators are averse to bearing false appearances for protracted time-durations or because they lack the ability to do so.
Physics for Marine Divinities
The clearest such indication of this is in the manner in which the Nereid Thetis and two of the Old Men of the Sea, namely Nereus and Proteus, are characterised. These three sea deities are each described as being in a state of habitual metamorphosis of a rather strange kind, even for mythical Greco-Roman characters. They were usually sought out for their prophetic powers. Typically some sort of nymph would reveal to a mortal hero seeking information from one of the divinities that he the hero would have to capture the god, whereupon he would be forced to engage in a wrestling-match against the deity.
The deity would transform him\herself into all manner of scary stuff like fearsome wild beasts, a torrent of water and even fire. If the mortal managed to hold on to the divinity until s\he had exhausted all his/her wild transformations, he would be considered the winner, the prize being an interview therewith. In the case of Peleus he was fighting to win Thetis's hand in marriage, in which venture he succeeded. Later on Menelaus managed to extract information from Proteus by employing the prescribed strategy.
Thetis and Proteus are each said to have become ravening beasts and fiery flames in their contests against these men. To me the most remarkable thing about the contests is not that Peleus and Menelaus won—extraordinary feats, to be sure—rather it is that they weren't mauled to pieces or burned to death in the course of the fights, nor indeed is there any indication that they were thereafter hideously maimed with injuries sustained from the deadly (or only seemingly deadly?) wrestling-matches. Moreover, how does someone hold on, tightly or otherwise, to a stream of water?!
Even for a fantasy story, the only way that this is logical, as far as I can tell, is that either these transformations are completely illusory (the deities are not in fact actually becoming snakes, lions, huge trees, or water or fire), or they are actually becoming these different things, albeit in an undoubtedly harmless fashion, either deliberately on the deity's part or because some law of nature is automatically protecting the mortal from being wounded through this process. (Alternatively, I suppose, the mortal might be getting magically healed at the end of these ordeals.)
It Won't Last Forever
Then there is the impermanence to which I was referring: Why don't these deities simply select one form in particular, say, the deadliest or most terrifying one, and stick to that? The implication is that they are not too heavily invested in winning at all (there is no story in which the deity wins, as it happens) and that it is merely a test of the mortal's mettle. Either that and/or they simply do not have the capacity to maintain a single feigned form for more than a few moments or, perhaps, hours.
A very similar phenomenon occurs in the stories about the Oceanid Metis and the goddess Nemesis attempting to ward off the advances of Zeus. They each assume various disguises but to no avail. To be fair, though, Zeus is notoriously relentless, and the maintenance of one form is shown to be no guarantee of escaping or overpowering him, such as it goes with the Titaness Asteria who simply becames a quail and can only get away from her would-be ravisher by being changed thereafter, permanently, into an island.
Nemesis is, on the other hand, according to Fragment 8 of the Homeric Kypria, joined to Zeus (her own father in this version) "by harsh violence" in spite of her attempt to escape him by assuming the form of a fish as well as sundry "dread cretaures" of the dry land, and fleeing all the way to the ends of the earth, "for shame and indignation vexed her heart." In Apollodorus' Bibliotheka, after she becomes a goose, Zeus becomes a swan and thus has his way with her. At any rate the king of the gods impregnates her with Helen, who is hatched from the egg that she lays in her bird form.
In an Orphic story about the origin of Persephone, she is the child of the Titaness Rhea by her own son Zeus. After Rhea has threatened Zeus in the form of a dragon, he too changes into a dragon and rapes her, forming some sort of mystical indissoluble knot in his tussle with her. Demeter is similarly raped by her own brother Poseidon when she attempts to disguise herself as a mare and he becomes a stallion. All these examples bear out an overtone of the ineffectiveness, to go along with the impermanence, of these metamorphoses.
On the other hand, whereas all the preceding examples involve failure on the impersonator's part, when a deity takes on the form of another deity, s\he is invariably successful in the deception s\he wishes to practise or in the similar objective that s\he sets out to achieve. There is only one exception to this, regarding which see the last section below.
Venus as Circe
Of all the following examples, only two do not occur in the Dionysiaka, and the first of them is technically not even Greek. In the Argonautica by the Roman poet Valerius Flaccus, Juno (the Roman Hera) wishes the Thessalian prince Jason (Iason in Greek) to succeed in the deadly tasks set for him by the Colchian king Aeetes, whose daughter Medea is a very powerful witch. Juno recruits Venus (the Roman Aphrodite) to cause Medea to fall in love with Jason so that she might be compelled to ensure his victory.
In order to bolster her influence over Medea, Venus appears to the Colchian princess in person but disguised as Medea's aunt, Aeetes' sister Circe (Kirke in Greek), who is an even more powerful witch. Incidentally Circe is also an immortal goddess (and as such she is referred to in Homer's Odyssey, Strabo's Geographia and Ovid's Metamorphoses). In the form of this goddess-witch, Venus pushes Medea to betray her father and help Jason.
Valerius Flaccus says that Venus gives unto Medea violent passion for Jason by clasping "the girl in her embrace," and
imprinting kisses that drive to frenzy... inspiring love mingled with
hatred
(hatred because Medea despises the notion of betraying her father for the sake of a man she doesn't even know). This implies that Venus is using her own "powers" as the goddess of love and that the only thing she has borrowed from the formidable divine witch is her appearance.
Poseidon as Enipeus
One of the most enigmatic examples is a story which Nonnus does not narrate but alludes to twice at the beginning (Book 1) and towards the end (Book 42) of his epic Dionysiaka. This is the tale of how Pelias (the king who sent Iason to Colchis) and Neleus were conceived. The Thessalian princess Tyro was in love with the local river Enipeus, who according to Homer's Odyssey was the most beautiful river on Earth, "to whose running waters," says Apollodorus, "she would often hasten to lament. Poseidon, taking the form of Enipeus, lay with her, and she secretly gave birth to twin sons," Pelias and Neleus.
In the Odyssey this took place at the mouth of the river, where
A dark wave, mountain-high, curled over them, and hid the god and the
mortal girl.
Presumably Tyro was able to appreciate Poseidon's disguise because she had seen Enipeus's divine form before. Nonnus implies that Poseidon appeared to Tyro as a horned bull, in which semblance river-gods often represent themselves in Greek myths.
The characteristics one would expect to be ascribed to appearances of Poseidon and Enipeus, both being gods of water and fertility, are so similar as to make it quite difficult to apprehend which differences between them Tyro might have recognised.
Ovid, in his Metamorphoses, has it that Poseidon impersonated Enipeus on another occasion, this time in order to consort with a relative of Tyro called Iphimedeia, who happened to be Poseidon's own granddaughter, and who bore him the massive twin giants Otos [Otus] and Ephialtes, famously known as the Aloadai [Aloadae, or Aloads].
Zeus as Artemis (or as Apollon [Apollo])
Three times (in Books 2, 33 & 36) Nonnus mentions the story of how Zeus disguised himself as Artemis in order to beguile this goddess's virgin hunting-companion Princess Kallisto [Callisto] of Pelasgia, who was Zeus's own great-granddaughter. Kallisto became by Zeus the mother of Arkas [Arcas], who when he grew up became king of Pelasgia and changed the kingdom's name to Arkadia [Arcadia].
Book 2 of Ovid's Metamorphoses recounts Kallisto's encounter with Zeus in some detail but it is narrated ambiguously enough that it is seems open to interpretation whether Zeus maintained his disguise during the rape or if he resumed his true form for the act. The most graphic portion of the scene is just a couple of sentences (between Lines 430 & 440) saying:
But when his ardent love was known to her, she struggled to escape
from his embrace. But how could she, a tender maiden, resist almighty
Jove {= Zeus}?
Even if the god had reduced his "power" so that it simulated only that of Artemis, presumably she would still be much stronger than the mortal Kallisto. According to Apollodorus (in Bibliotheka 3.8.2), "others say" that Zeus masqueraded as Artemis's twin brother Apollon rather than as Artemis.
Zeus as Haides [Hades]
In Orphic Hymn 70 to Melinoe, Zeus disguises himself as Persephone's husband, his own brother Haides, and impregnates her with the frightful Underworld goddess Melinoe. Apart from the example from Valerius Flaccus, this is the only other one of these stories which, curiously, does not appear in Nonnus. In fact Melinoe does not seem to be attested anywhere else.
Nike as Leto
In Dionysiaka 2, the cosmic hundred-headed, two-hundred-armed giant Typhoeus attacks Heaven, and Zeus rises to the challenge of defeating him. The night before the final battle between Zeus and Typhoeus, the winged Titaness Nike, who is the personification of victory, disguises herself as another Titaness, namely the goddess Leto, who in Hesiod's Theogony is the last in Zeus's series of six wives before he settles down with Hera. Leto is also the mother by Zeus of Apollon and Artemis.
Nike assumes this form in order to encourage Zeus to ante up for the imminent fight. Presumably Leto is usually especially soothing for Zeus to listen to when the going gets tough(?).
Nike is quite low in rank as a goddess but from the description of her and her siblings, she sounds like she would be one of the mightiest beings in the universe, and thus why it is so useful to have them (Nike and her siblings, i.e.) as Zeus's royal bodyguard. Nike's brother Kratos [Cratus] and sister Bia are literally Might and Violence themselves. It is difficult to evaluate who is "mightier," therefore, between Nike and Leto, not that it makes much of a difference in this scenario since all that Nike does as Leto is talk to Zeus before going back off-screen.
Eros as Seilenos [Silenus]
In Dionysiaka 11, a young Satyr named Ampelos [Ampelus], whom Dionysos [Dionysus] has befriended, dies a violent death. As Dionysos mourns him, Eros disguises himself as Seilenos, the elderly drunk god who is a member of Dionysos' entourage, and he attempts to console the young wine-god with a story.
Hermes as Dionysos
Dionysiaka 35 begins after a large number of women from Dionysos' retinue, some of whom are called Bakkhantes [Bacchants], have been captured and driven into the stronghold city of King Deriades of India, against whom Dionysos is at war. Over the course of the preceding few books, Hera has organised a scheme causing Dionysos to reel in helpless madness while his army is thrown into disarray.
After many of the women have been killed, Dionysos' half-brother Hermes—who has, since the wine-god's infancy, played guardian to Dionysos—comes to the women's rescue.
For swift-winged Hermes came in haste from Olympos [Olympus], wearing
a semblance like the face of Bromios [an epithet of Dionysos] and
summoned the whole company of Bakkhantes in his mystic voice. When the
women heard the divine Euion sounds, they gathered into one place;
the swift-sandalled one brought them from the triple-ways and led the
whole tribe of Mainalides by crooked winding lanes until he was near
the walls.
Then furtive Hermeias [Hermes], the warrior by night, with his
all-charming rod shed refreshing sleep on the unresting eyes of the
guards in order. Suddenly for the Indians there was darkness; for the
unseen Bakkhantes there was light unexpected. The women made no noise
as Hermes led them secretly through the city without his wings.
Lines 227-239
Hermes then ushers the women out of the city. The "all-charming rod" here is Hermes' famous herald's staff, which has the power to confer sleep upon someone or to take it away. As with Venus becoming Circe in the Argonautica, Hermes seems to be using his own powers rather than those of the wine-god, although he avoids using his own ability to fly because he is trying to maintain the illusion for the Bakkhantes and their fellows that their master is the one rescuing them.
Hera, Potentially, as Themis, Aphrodite and Artemis
In Dionysiaka 31.118-120, Hera, while instructing her herald Iris to impersonate Nyx, reveals that she herself, apparently quite often, assumes the forms of other goddesses, though she fails to supply us with the reason for this habit,
since I also change my limbs into the aspect of Themis or Kythereia
[an epithet of Aphrodite] or Artemis when need compels.
Nonnus calling Hera "all-seeing" or saying that she has "infallible eyes" seems to be hyperbolic praise, or some form of deliberate irony, since, in the same story which refers to her like that, she allows someone to get past her because he has fooled her with a disguise.
THE FORM OF A MIGHTIER ONE
Iris as Ares
In Dionysiaka 20 Hera sends Iris on "an evil errand" to incite King Lykourgos [Lycurgus] of Arabia to fight against Dionysos. Iris achieves this by replacing "her embroidered saffron robes" with a plumed helmet and bloodied armour, under which she bears the appearance of the war-god Ares.
She speaks to the king as though he is a son of Ares, even though in other accounts, as well as in this same one, his father is a mortal named Dryas. There is, however, a Dryas, who would have lived generations later, who is said to have been a son of Ares. Perhaps Nonnus is here conflating the two so that the implication is that Ares is Lykourgos' grandfather. In Line 168, though, Nonnus explicitly says that Lykourgos is a child of Enyalios (an epithet of Ares). In Line 220 Lykourgos is called Hera's grandson (because Ares is Hera's son).
At any rate the conversation been Iris (as Ares) and Lykourgos certainly implies much familiarity between the war-god and the Arabian king, the latter of whom has been sacrificing wayfarers to Ares, in whose honour he affixes the heads, hands and feet of his victims to the gates of his citadel. By all other accounts this Lykourgos is king of the Edones of Thrace.
Nothing in the interaction here suggests that Iris takes on Ares' powers, and in fact the detail about her wearing a helmet and some pieces of armour as part of her disguise are an interesting touch of what we might recognise as modern-artistic realism, implying the possibility that a deity could fail at pulling off a convincing impersonation somehow. After the meeting, which involves merely talking, the fake Ares turns into a falcon and takes off.
Iris as Nyx
Back to Dionysiaka 31, where, as aforementioned, Hera has her messenger Iris impersonate Nyx, who is the primaeval personification of night-time. This is done in order to convince Nyx's son Hypnos, the personification and god of sleep, to plunge Zeus into deep slumber so that Hera can harass and devastate her illegitimate stepson Dionysos without Zeus's intervention into her schemes.
Nonnus copies virtually all the ideas in this sequence from Book 14 of the Iliad, wherein Hera herself convinces Hypnos to do the exact same thing to Zeus while she harasses another illegitimate stepson, this time Herakles [Hercules], generations after Dionysos' adventures. Nonnus' innovation here is, incidentally, this thing about an impersonated Nyx being needed to persuade Hypnos to do Hera's bidding.
Hera commands Iris to "take the ugly form of Sleep's mother the black-girdled goddess Night; take a false name and become darkness". In obedience to this:
Then Iris changed her shape, and all unseen she put on the look of
dark Night unrecognisable. She came near to Sleep, weaving guile; and
in his mother's guise uttered her deceitful speech in cajoling
whispers.
Iris then makes an argument for why Nyx is neglected, and in indignation Hypnos swears to do as she asks.
In the Iliad, Nyx is feared even by Zeus himself. She is almost as ancient as Phanes is. In this Dionysiaka scene, all that Iris does while disguised as her, just like when she impersonates Ares, is talk. On both occasions Iris is masquerading as the parent of the character to whom she is sent to persuade the individual to do something dangerous.
A Central Theme
In every one of the above-mentioned examples which Nonus fully narrates (namely of Nike, Eros and Iris, and apart from the one of Hermes appearing as Dionysos), the author's focus is on the chunk of dialogue spoken by the disguised personage, which then invariably spurs to action the character to whom the speech is delivered.
The phenomenon recurs with Venus as Circe in the Argonautica; and even in the Hermes-as-Dionysos episode it is still important to Nonnus to mention that Dionysos' "mystic voice" and "sounds" are the means by which the Bakkhantes become convinced of their master's presence among them.
THE MIGHTIEST OF THEM ALL
Zagreus as Zeus and as Kronos [Cronus]
The Dionysiaka relates an elaborate account of the conception, life and violent death of the beautiful, monstrous, shape-shifting baby god Zagreus, an Orphic deity who centuries later is reincarnated as Dionysos. Like Dionysos and Herakles, Zagreus is a favourite but illegitimate son of Zeus whom Hera passionately hates and seeks to destroy. Unlike with Dionysos and Herakles, Hera succeeds in effecting Zagreus's fatal doom.
In Book 6, Hera sends certain of the Titans to do her dirty work for her, and they chop Zagreus to pieces with "an infernal knife". The elements of the scene are very interesting to the purposes of this Question, concerned with illusion and self-perception, and how these connect to power.
The Titans are able to corner Zagreus by covering their faces with chalk and by showing him a mirror, which seems to be some sort of a big deal because, even though he is just a baby, Zagreus quickly becomes aware that his life is in danger and launches into a series of metamorphoses which by the end prove useless against the onslaught.
Zagreus's first instinct is to transform his appearance into that of his own father Zeus and try to scare his attackers off by shaking Zeus' Aigis [Aegis] (or just something that looks like the Aigis?) at them. Then he appears as Zeus' father "ancient Kronos, heavy-kneed, and pouring rain." After those two divine disguises, Zagreus becomes a baby, an adolescent boy, a roaring lion, a wild horse, a snake, a tiger and then a bull.
With the sharp horns of his bull-form, Zagreus attempts to gore the Titans, but then Hera, who is watching from a distance, emits a bellow so loud that it causes the Zagreus-bull to collapse. The bull then gets slaughtered.
The Titans seem not to be fooled into thinking that Zagreus is actually Kronos, nor are they moved by his impression of Zeus, which appears to have been less formidable than the bull-form which the baby god assumed. Hera seems to have thought that Zagreus could do more damage as a horned beast than as Zeus or Kronos, which is quite revealing!
There are a few aspects of this story which, on different levels, set it apart from the other examples. It is Orphic and thus is even weirder than the more mainstream myths: Zagreus is Dionysos but also sort of not. The divine shape-shifter character in this case, even though he is a god, is mortal, and the only way that Zeus can think to bring him back is to reincarnate him as yet another son of his own (connecting to striking parallels with a basic trope of Hindu mythology).
Maybe Zagreus was mortal only in beast-form, or he was "in character" so deeply that he actually became a bull (one that could die).
Unlike the other shape-shifting deities we've looked into, Zagreus is an infant and perhaps his understanding is merely that of a baby, meaning that he might be less powerful than Zeus and Kronos. Alternately, might Nonnus intend to be asking us, subliminally: What if the kid was given a chance to grow up? He could have been the mightiest of them all(!!)... mayhap?
Indeed, part of what freaks Hera out about the little one is that Zeus had placed the newborn on his own throne and let him play with his thunderbolts like toys, indicating plans to abdicate in his favour as king of the gods.
The complete narration of Zagreus's life, from birth to death, is contained in a few paragraphs: see Dionysiaka 6.155-228.
