Yes you could get a cheap version repeater or booster which can take a cable but from what I seen they still don't work well so you could just get another router with onboard WiFi and connect that with maybe a small amount of changes in settings
This is cheap way of doing it
As swb said access point, but decent ones cost money
A switch with an access point is possibly the term your looking for. Or maybe just an access point plugged into the current switch.
Every site is different when it comes to WiFi signal, so many variables to work with.
In a standard house the router is often in the worst place for WiFi signal due where the master socket is.
Often disabling the WiFi at the router and having a decent wired access point in a central location best solution with minimal kit cost.