A common theme in older novels and some more modern publications is that of body parts (potentially from multiple species) being 'swapped' on to new bodies and recombined in (usually grotesque) ways by mad scientists (I prefer the term misunderstood, personally, but that's just me).
An example of this would be Frankenstein's monster: sewn together from multiple corpses and yet seemingly functioning without any real issue (ignore the fact that the monster was mostly made from dead flesh and assume that the body parts in question are relatively fresh). Some depictions of Doctor Moreau also include monstrosities constructed from multiple animal species, crudely reshaped by the whim of man.
In the real world today we often perform transplants of organs, skin and even limbs, but these may require life-long drug treatments to prevent rejection, and they are limited to one species (preferably close relatives) or organs that have been heavily altered using highly complex methods.
Bearing this in mind: What would have to be different about the biology of mammals (for example lower immune response, better sugar regulation, all identical blood types) in order to allow far greater inter-compatibility, and how far can this compatibility be taken?
Preferably any hack with a basic understanding of the cardiovascular, skeletal and nervous systems should be able to cobble together his own pet abomination of nature by sewing the right bits in the right place and adding a few bolts to hold the bones together, but since biology is terrifyingly complex I'm willing to accept that this may not be possible, though I would like to see how far the concept can be taken for
my next experiment's sake my own satisfaction.