Integrate ring doorbell with old doorbell

Hi. I have an old Victorian door style door bell push which is moulded into the outside of the house entrance. Removing this would look quite messy and would be a shame to remove this original feature. v I also have a Ring door bell which is being separately wired for use on the same door (although is currently battery powered). Some people press the old door bell rather then the Ring door bell. Is it anyway possible to integrate the old door bell push to the Ring doorbell system? I am surprised this isn't a common problem in the UK, but couldn't see any other posts regarding this. Thanks.