In Harry Potter and the Deathly Hallows, just before the Battle of Hogwarts begins, McGonagall conjures multiple Patronuses to alert other teachers. After learning that summoning multiple Patronuses can be done, I was curious if it was possible for a witch or wizard to summon multiple Patronuses that were entirely different animals, like one Patronus is a deer, and another one is a bear. Is this a thing that can be done, or is it just one specific animal?
The Patronus is very advanced magic and not all witches or wizards can produce one. Some can produce only an incorporeal Patronus which is less powerful.
McGonagall produced three cats to send a message to the other heads of houses but there appear to be no instances of anyone producing multiple Patronuses with different forms.
Harry Potter: "What does a Patronus look like?"
Remus Lupin: "Each one is unique to the wizard who conjures it."
Although Snape’s was of course the same as Lily’s due to his devotion to her.
No, it is not
Patronuses take the form of an animal which closely resembles something about the caster's character, often buried deep under their subconscious. For example, we see that for Animagi, the corporeal form of their Patronus matches the animal they turn into.
The mechanics of the Patronus charm is not something that has been explained in canon, yet we usually see animals that are relevant with the characters that cast them (e.g., all Potters have Patronuses in the family of stags, Remus Lupin, a werewolf, has a "wolf" Patronus, etc.).
Patronuses can only change unintentionally
However, the form of a corporeal Patronus, cannot change at will. The only possible way of it ever being changed, is pure love:
.@tigs25 Your Patronus only changes if it's eternal love, unchanging - part of you forever.
J.K. Rowling on Twitter
Incorporeal Patronus, can be employed
If someone wishes to "stealth" use their Patronus, like the scenario you described, they can choose to cast an incorporeal Patronus at will. Lupin does this the first time Harry faces a Dementor:
‘Professor Lupin stepped over you, and walked towards the Dementor, and pulled out his wand,’ said Hermione. ‘And he said, “None of us is hiding Sirius Black under our cloaks. Go.” But the Dementor didn’t move, so Lupin muttered something, and a silvery thing shot out of his wand at it, and it turned round and sort of glided away…’”
Harry Potter and the Prisoner of Azkaban
The fact that Lupin has a corporeal Patronus but chooses to hide it, is confirmed by J.K. Rowling herself:
Remus’s Patronus is never revealed in the Potter books, even though it is he who teaches Harry the difficult and unusual art of producing one. It is, in fact, a wolf – an ordinary wolf, not a werewolf. Wolves are family-orientated and non-aggressive, but Remus dislikes the form of his Patronus, which is a constant reminder of his affliction. Everything wolfish disgusts him, and he often produces a non-corporeal Patronus deliberately, especially when others are watching.
Remus Lupin, Wizarding World - by J.K. Rowling