Breaking and reassembling model is not really possible because 3d models are just hollow surfaces they have nothing inside.

I guess at most what can be done relatively easy is to use some kind of building blocks that have several flat, non bending surfaces and you can attach other blocks to those surfaces. so you could stack shoulders or torsos on top of each other to make human centipede
or replace hands with heads

I woud say that Minecraft is closest to this concept

something similar is already done in 3d modeling software like daz3d under that mane of "geografts"
however this system does not allow to place anything anywhere you need co construct replacement for single specific place of attachment my matching loop of vertices.

determining character capabilities is practically impossible because you cant even tell what kind of behavior will be optimal for that character.
like if you replaced legs with hands it will be hard to decide if it is better to move on all four or just use 2 hands as legs and keep other 2 free.
not even mentioning issues with bending and strength differences in different positions.
Imagine how woud it feel if your legs were placed backwards, it woud be hard to predict how that woud work.