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How to put a router with DHCP between my computers and the modem while keeping the 192.168.0.x addresses?

My internet provider has occasional issues and the modem that is a DHCP server for my computers leaves me without a local network until their issue is resolved. So I figured if I put a router (with a DHCP server and disable the DHCP server on the modem) between the computers and the modem I can keep my LAN on while the modem is off. I don’t want to change the IP addresses of the computers that are now 192.168.0.x so how do I do that correctly?