Subnetting question

We have run out of addresses on our 10.0.0.0 class A subnet due to wireless connections in DHCP.

Without using an additional router how can we add the 10.0.1.0 network for wireless connections only?

Why cant I setup a server with a static address of 10.0.1.2 with our default 10.0.0.1 gateway and use this as a DHCP server for the 10.0.1.0 network? The wireless clients really only need internet access, which would be provided via the gateway listing.

They would need to access printers on the 10.0.0.0 network. Since both networks would be on the same 24bit subnet mask, I do not understand why this will not work.

Again, we would prefer not to use additional routers for this configuration.

Thanks for any help!