We are looking for a solution to allow certain employees to merge Support Cases without allowing them to otherwise delete Support Cases. Anyone tackled this before?

Assuming there is a permission that does the above, in the instance you have to have the permission fully enabled, you could script a deny for the deletion.

In order to merge you need the permission to delete, because merging deletes one of the cases.

Meaning that on a delete context for user or role, throw an error message to the user and block that action from completing. It might be possible with a WF, definitely possible via script.