Help with router issue

I work for a very small company who is just now thinking about networking. I am self taught on computers and networking so I know what is the best way to go but they can’t afford it right now. We use webhosting right now even. My problem is our DSL router doesn’t have enough ports to service our needs. We need at least 10 ports. I wondered if I could buy a second router and run an out line from the first into the second? Please let me know if this is possible.