The easiest solution would be if the router (OI side of the wireless) supported the 255.0.0.0 subnet mask. If it did you would be able to have a 10.xx.yy.device network and a 10.aa.bb.device network. Unfortunately the router we were supplied with will only support a 255.255.255.0 subnet mask.
The reason this would work is that the subnet mask defines what IP addresses the router routes. For example if your routers IP was 10.99.99.4 (team 9999) with the subnet mask of 255.255.255.0 it will only look for devices with 10.99.99.x IP addresses on the LAN ports. If the subnet mask was 255.0.0.0 the router would look for all IP addresses starting with 10.x.y.z.
If you had a router that you could setup with a 255.0.0.0 subnet mask you would be able to setup 2 separate control systems on the same router as long as each control system had individual "team number" IP address sets. The router would just have to have any 10.x.y.z address.
Let me know if you have any questions on this. I would love to explain it more if needed
...Forest Immel