Not really enough information
If you are establishing a private network using a private address range
10.0.0.0 through 10.255.255.255
169.254.0.0 through 169.254.255.255 (APIPA only)
172.16.0.0 through 172.31.255.255
192.168.0.0 through 192.168.255.255
So the network is on your own WAN/LAN link??? example below
Your Network>>>>>Router——————-WANLINK——————Router>>>>>>>>Other Company
you dont say what servers you are using? If Windows you will have to create trusts between the sites.
Installing two network cards? not sure if this would work depends on your WAN set up.
If you you are using Windows you can add another IP address to the same card but this will cause issues.
Please provide more info
You need to first throw a firewall in there with a public address, and then allow the firewall to give out private ip addresses to your internal network . This way you can allow the other private networks to communicate with your network via the rules setup in your firewall. I would never allow my ad server to be viewed by the other networks without having a firewall in between.