Can A Router Connect To A Switch To Gain Additional Ports

Can a router connect to a switch to gain additional ports (to both access the internet AND to maintain an internal / home network)?IP line to house, connected to modem, connected to 4-port router, connected to 8-port switch. Now, each of six rooms in my house has one Cat-5e (RJ-45) jack whose run terminates to the switch. In some of these rooms, I need two wired devices (wireless isn't an option for the devices). Can I use the LAN port of a spare, wireless router (to also use as an access point for cell phones, etc) to plug into the jack and increase the number of ports in that room to have a functional LAN and WAN? I have read tons of info on plugging switches into routers to increase the number of ports, but not the other way around. Plus, ripping open walls to expand the network isn't feasible either. My other thought, would be to replace the switch with another (2nd) router, by connecting the 1st and 2nd routers together, and have the runs terminate to the open LAN ports of both routers --= and then expand the ports in those rooms by also using additional, spare wireless routers.