Time machine/airport

Just to be sure we are talking about the same things. Time Machine is an Apple app that allows your Macs to make periodic backups. A Time Capsule is an Apple wireless Internet router that has a built in hard drive which is designed primarily to be a destination for those Time Machine backups.

I am assuming by "time machine" in your post, you are referring to the Time Capsule. If so, then yes, it may be possible to use it in conjunction with another router.

Time Capsule will generally work fine plugged into another router and setup in bridge mode. Just ask if you need the details.. but we have posted it many times if you bother to search.

There are a few tricks to making it reliable.. so do ask with all the info about your current main router etc.

Apple is moving away from using local network backups it seems so people on big (bug) sur are having plenty of issues. Don't be surprised.

To extend the answer as Tesserax has covered our usual confusion if you mean Time Capsule or Time Machine; A very few routers do support Time Machine to a USB drive plugged into them.

Asus and Synology are two that I have used and tested. The later being better (more reliable) for Time Machine but the Asus makes a better router. Also not sure Synology has long term plans to stay in the business.. they have no announcement of a WiFi 6 router yet.