A connection is identified by the tuple {host IP, host port, client IP, client port}. The server listens on one port, but the client has a separate port for each connection. This means that there can be 65k connections for a single {host IP, client IP} combination.
There's two ways to get more connections: use more client IPs or use more host IPs. In this post the OP has decided to add more host IPs.