adding mesh to an existing router

I am looking to add a mesh to my existing home network. I have ATT as the ISP and they provide a combination modem/router. Can I plug the primary mesh node into (using the Ethernet cable) my AT&T provided router/modem combo? Or do I need to replace the existing router? And if it does plug into the existing router, will the mesh SSID be the same as the existing router?

I am looking to provide a level of indirection for my home network with the SSID such that I don't need to change all the connecting home devices when/if I ever change the ISP. Almost unbeknownst to me we have accumulated ~14 devices connected to the home WIFI and it is a royal pain to go about changing all of them when the ISP changes. I believe having a mesh will provide this (in addition to the blanket WIFI within the house).

Thanks much for your help!