You need to mesh merge.
This is probably no different than a modular character, just at a much larger / possibly unsustainable scale.
You need to review the eu4 docs on it, and implement the thing via C++.
Im assuming you have some sort of creation screen where the assembly happens instead of a base building system.
Once merged, pieces arent individualized for moving/changing, so you need to keep versions of the model separate.
One that is editable and contains the components.
One that gets merged and used in game (without any of that extra data).
As a basic in engine example, you can throw a billion pieces into PIE, get 2fps and assemble the object.
If you then select all of them and merge the actor you get back to max fps / 1 drawcall or a lot less, one per material.
The difference is you want this to be something that can happen at runtime - and the system will end up hanging thr game thread when processing, so you really need to read up how to make non game-blocking threads, move the computation bit there, and present the user with a loading screen or even allow extra gameplay while conputing happens…