Video doorbell 4 and existing dumb doorbell in parallel?

Hi Folks. I’ve searched for information of the possibility of having an existing dumb doorbell push switch, existing transformer (if suitable) and existing dumb chime powered in parallel with a video doorbell 4. I cannot find a wiring diagram for this scenario. Would I need a module or diodes to get this to work. It’s very difficult to get new wiring to where the video doorbell 4 is, but the old bell push is only 6” below. I want both bell pushes working independently of each other. I’m sick of having to swap the battery every three weeks. If I decide to go on holiday for more than three weeks, I lose the option of “answering the door” when not at home. Any ideas? Thanks in advance!