Fiber & Modem Question

Hi I have a small question

So we just got a new fiber connection, which has a box on the wall inside the house, which is then plugged into the modem

Now this box has more ethernet ports, so i wanted to know if i buy a third party modem from store, can i plug it into the fiber box? will the modem then be capable of getting internet, or will it not work ?

i just thought i will use a 2nd powerful modem for pushing wifi into the back rooms, as the current rooms dont get enough from existing modem which is given by supplier,

cheers,