Verizon FiOS TV → Re: [STB] Ethernet to COAX to get rid of cables going through whole apartment

is it possible to split the fiber and run another actiontec modem in other room?

The fiber does not connect to the Actiontec, which is a router, not a modem. The fiber connects to the ONT (Optical Network Terminal), which connects to the Actiontec using an Ethernet or coaxial cable. It is however possible to run a second Actiontec in another room by following this guide on the FAQ:
»Verizon FiOS FAQ »Can I get an ethernet connection in a room with only coax?

Last year there were announcement by Verizon about Magic Wire. Haven't heard anything since, but someday we may get what you want.

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