Well, this is a big problem. Subdivision deforms the mesh, it can work fine on a closed continuous two manifold surface, but if you have a discontinous surface you have the risk to have the mesh broken after the subdivision because two vertices that had originally the same value will deform in a different way.
I have experimented Catmul-Clark and loop subdivision with Victoria 4 and the result looked much worst than the original Vicky even she was all welded.
The only subdivision that has preserved her shape was middle-point that only increased the number of faces without degrading the figure.
You can ask me for what increase the number of polygons if the shape continue to be the same?
For magnets, the morphs can be more precise where you need!

Stupidity also evolves!