No you can't run more than one modem in the same line. Well, in theory you could but not in practice. Best option for you is probably a power line adapter. You plug the adapter to a regular wall socket, connect the ethernet cable and you plug another similar device to the wall socket in another room. It works basically like an ethernet cable but uses the existing power cables.You can get decent speeds that way and it supports multicast etc. protocols which may not work so well on wifi. http://www.cnet.com/topics/networking/best-networking-devices/power-line-adapters/
You can run two modems off the same coax but if you are using them both for internet, the ONLY way this would work is if both have their own internet service. So for example if you are paying $40 for internet service to one modem, you will pay an addl $40 per month for service to the second modem which would double your bill. In the long run you would just be throwing money out the window where there are much cheaper options to use
Best option for you is probably a power line adapter. You plug the adapter to a regular wall socket, connect the ethernet cable and you plug another similar device to the wall socket in another room. It works basically like an ethernet cable but uses the existing power cables.You can get decent speeds that way and it supports multicast etc. protocols which may not work so well on wifi. http://www.cnet.com/topics/networking/best-networking-devices/power-line-adapters/
Over existing coax, MoCA adapters are likely better choice. Not as cheap as powerline, but not as problematic either.
Not all rooms have coax pulled to them.
What all rooms have got to do with? He said he got coax in his office.
Maybe I'll go knock on their door sometime this week lol.