I suggest doing something with CollisionGroups, maybe when the player holds the object, the object becomes part of the CollisionGroup of other held objects and only the held objects can collide each other.
Most of those systems for example lumber tycoon 2 seem to use a some sort of bodymover(mostly bodyposition) which manipulates network ownership to make the part seem smooth for the client but not for others. This means you will not have to worry about parts clipping.