Mechanical Chime w/Ring Power Adapter

Hello, Just a quick question with regards to the Ring power adapter. I have a Ring Doorbell Pro hardwired to a mechanical chime. I noticed that there is not enough power for the doorbell to function properly. I can't seem to locate the transformer, therefore I can't upgrade the power via new transformer. My question is, can I connect (hard wire) BOTH the mechanical chime and Ring power adapter together, or is it one or the other. Thanks,