non-destructive editing of a sharedmesh

I have a SkinnedMeshRenderer for an asset built in max (fbx format), it is a rigged mesh. I need to be able to modify the mesh itself, i.e. the base mesh, via script. I tried editing the vertices attached to the sharedMesh in the SkinnedMeshRenderer, but this destroys the mesh of the original asset. Is there a correct way of non-destructively modifying the mesh for a rigged model?

For example, do I need to somehow clone the entire model (copying the data from the asset)?

I need to do this in script so that I can personalise the asset to the player at runtime.