Outside FiOS box means Optical Network Terminal (ONT) should always be directly connected to FiOS Router. ONT has direct connection with OLT (Optical Line Terminal), Verizon office.
Reason:-
First off, NAT (Network Address Translation) should be completed on the router and only then the clients connected to the router (wired or wireless) devices will be able to obtain Private IP addresses from DHCP Server.
However, you can connect switch to the BHR (Broadband Home Router) once a connection has been established between ONT and FiOS Router.
Network Diagram:-
O L T. - - - O N T - - - FiOS Router- - - Switch