Is sever to sever communcation possible?

I want to do server to server communication using clients.

I build two separate dedicated server executables. Both exist as a client and a server.

Let’s say I have two separate machines. Both have the dedicated server executable. I run both on each. Is it possible to have one communicate to the client of the other?

Server/client (A) > client/Sever (B)

Server A talks to Client B which relays to Sever B. Is this possible? If I have the same game state?

The general idea is to chain this. To emulate peer to peer networking. But first I have know if this is possible.