Can I keep adding routers???

Okay, I got a question. I'm not into all that "network" stuff, but here goes.

I have a 4 port router connected to a cable modem. Originally, we had 4 comps. We ended up with 6 comps, and we're trying to figure out a way to expand. I want to know is, can I just "add" another router. In other words, the cable modem will be connected to the 4 port router, 3 computers to the 3 ports, and the remaining port connected to another 4 or 8 port router. And so on. Can I do this???

got any good choices for one?? I don't really know the first thing when buying a hub or switch.

Connect a 4 port switch to one of the ports in the router. I did that myself and it works just fine. I have a router downstair with 2 computers, and another 2 upstairs. Instead of running another line, I got myself a switch.