Can I use other router as main and add Quantum gateway router?

Hi Everyone,

I have Fios gigabit service and Quantum gateway router. I would like to know if I can use other brand router(non-wireless) as primary and add gateway router as second. 

Here is the story. 

We have a ethernet cable box in basement where controls all ethernet ports in house. I would like to use wired connection in some rooms so I have to put 1st router near cable box in basement. If I put quantum gateway router in basement, signal will be  too weak for upstair. So I am wondering if it is possible to put some cheap router in basement and run cable to Quantum router which will be in 1st floor. Would this work? Or should I get 2 Quantum gateway routers? 

Thank you for your help everyone!