Sure, you can certainly chain as many routers together as you like, and they’ll all work just fine so long as they’re not all trying to hand out DHCP addresses within the same range. You can either disable DHCP on all of the routers but one, and allow the other routers to effectively function as switches, or you can set each router to hand out addresses within a different range, which will essentially give you double-layer NAT functionality…but when you run into firewall issues, it becomes a little less clear where the issue is, and opening up ports for unfettered Internet access becomes just a bit harder. If you haven’t bought the second router yet, you could save a few dollars and make the process easier by using a switch instead — anything connected through the switch will automatically retrieve IP addresses from the first router.