I presume your EA-N66 is wirelessly connected to another router upstream?
If that's the case, sure, you can connect a wired router to the EA-N66. However you'll have to configure the router as a switch - turn off DHCP, turn off the firewall, turn off NAT, etc. Plug the EA-N66's LAN port into one of the LAN (not WAN) ports on the router, and plug other equipment into the router's other LAN ports.
If that's the case you might as well just get a switch, because that's all this second router will be doing. Wired switches are quite cheap these days, I keep seeing a 10/100 5-port one that's free after mail-in rebate.
I'm guessing you're considering this because you have a surplus router on hand though. Just make sure it doesn't duplicate any of the services your main router provides. It usually won't get an IP address by DHCP if you use its LAN ports though, so assign it an IP address outside your DHCP pool first or you'll have trouble accessing its web interface (which you'll need for turning off all its services). Do this by connecting it directly to a computer and manually reassigning its IP address first, because if you just connect it, it may try to use the same IP as your main router which would cause lots of problems.