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You can do that fairly easily.
You can disable wifi on the Verizon router.
Connect your personal router from an ethernet port on the FIOS rotuer to a Lan connection on your router.
Set up your router to no do DHCP.
Set up wireless how you like on your router.
This turns your rotuer into a wireless bridge.
Should work just fine.
i am new what are old routers vs new router models
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