I've seen a photo in Twitter claiming that someone managed to make an art out of immigration stamps, as follows:
Is it really possible to ask immigration officers to stamp in a certain way to end up having a similar art?
This is not a photo of a real passport, it is a composite made for an ad campaign for Land Rover.
Genuinely producing such an artwork seems quite implausible to me, since border officers will want to place entry stamps so that the date of entry is legible, since that's the whole point of the stamp. While it's common to ask them to stamp on a specific page to save space, a request to stamp on top of an existing stamp will almost certainly be refused.
If you have an old passport, that has been properly invalidated by the authorites (they cut off a corner where I live, I suppose that's the common practice), then you could ask the border officer if he might be willing to help your art project out by placing a stamp in the old one.
They might still refuse, accept that and move on. Also, do the rest of the world a favor and don't ask this when there's people waiting behind you.