I'm a techie, and with Verizon fios (or frontier if you have them), you cannot use your own modem. You have to use theirs.
HOWEVER you should not be renting their router (the thing that makes wifi), you should use your own router.
If you have issues with signal strength, I'd get two routers and make one an access point (which means it connects to the wifi of the router that's on your modem, and broadcasts it's own wifi), and then they'd work together.
For faster speed on the second router, if it's feasible for you to run ether an ethernet cable to it, that would be your best bet.