That's exactly what home broadband routers such as the Linksys BEFW11S4 do. Their "Network interface A" is configured using DHCP -- with the DHCP server usually being at the ISP -- and they have a "Network interface B" that you can configure yourself. (Often they have a four-port switch on B. And they usually have a DHCP server for the B-side built-in.) You might have to configure a manual IP address (not DHCP) on network interface B, but the rest of the 10.x.y.z network can still use DHCP, and apart from that it does what you're after.

Peter