Adding Ring Video Doorbell Wired to existing 1st gen Ring Video Doorbell

We have a 1st gen Ring doorbell hardwired to the existing doorbell at our front door. We are looking at getting another Ring for the back door which still has the existing doorbell. Both doors use the same chime and transformer. I've not been able to find any information on whether you can mix a wired Ring with a hardwired battery Ring on the same 40VA doorbell transformer. Has anyone tried this?