An Animagus is supposed to be able to transform itself into the animal that most suits its personality.
Since humans are animals, what if it transforms himself into another human?
No
This is not supported by canon, just my humble thoughts. But I think it's reliable.
An animagus doesn't just take the appearance of an animal, he becomes this animal. When transformed, the animagus keeps his special traits. Wormtail doesn't recover his lost fingers when in rat form, Rita Skeeter has some marks near the eyes that remind her glasses when in beetle form, and so on...
‘[...] Look very closely, and you'll notice the markings around her antennae are exactly like those foul glasses she wears.’
Harry Potter and the Goblet of Fire, when Hermione reveals that Rita is an Animagus
And in PS, chapter 1, description of McGonagall:
a rather severe-looking woman who was wearing square glasses exactly the shape of the markings the cat had had around its eyes.
And again in PoA, chapter 6:
[McGonagall] transformed herself in front of their eyes into a tabby cat with spectacle markings around her eyes.
By this, I understand that their appearance when in animal form is the appearance they would have had if they were born this animal. (Doesn't make sense to you? Yeah, I'm not sure either..)
So if an Animagus transformed into a human, he would take the appearance he would have had if he was born human... But wait ! He actually was born human ! And this appearance his... himself. Pointless.
What you're may be talking about (taking anyone appearance, or at least modifying your own appearance) is what a Metamorphmagus can do, like Tonks.
In an interview with JK Rowling (Edinburgh "cub reporter" press conference, ITV, 16 July 2005):
You see, you do not know what you are going to be until you have done it, so you might spend half a decade trying to turn into an animal and then find out you were a slug or something, which would be most unpleasant.
Ablus Dumbledore's Commentary after "Babbity Rabitty and Her Cackling Stump" (The Tale of Beedle the Bard) describes Animagus as
. . . human-to-animal transformation [that] requires much study and practice...
That suggests that human-to-human transformation would not be an example of an Animagi.
It is impossible, since Animagi can only transform into an animal, and only one type of animal.