You can split a shared vertex into multiple vertices (one for each polygonal face that shares it) using the Detach Component feature. You can then perform independent operations on the split edges.
Splitting a vertex that is shared lets you separate the edges of the faces so you can create an opening in a polygon mesh or divide the polygon mesh altogether.
The Detach Component feature ignores selected vertices that are not shared.
The selected vertices get split into multiple separate vertices that are not shared.