To properly support multiple objects in edit-mode, we will have to move evaluation data data out of the shared EditMesh structure. See T85974: Edit-mode undo/redo causes assertion.
Note that to properly support this we'll have to remove EditMeshData isn't thread save.
This patch could be extended to do this, in the short term it's simplest to disallow multiple objects sharing data to be in edit-mode at the same time.