Monitoring multiple server behind one public IP

Nagios
1

Is it possible to monitor multiple servers on a private network behind a firewall with 1 public IP?
My Nagios monitoring server is on the public IP in a different location.

I usually do port forwarding from the main IP of the gateway to the private IP of a server behind it.
I thought of port forwarding from a different port than standard 5666 to the internal host’s 5666, but how to configure Nagios to query this different port?

2

Some of the nagios plugins may not have an option to specify a port. It would be best if you setup nagios in the private ip network with NSCA and forwarded the data to the central nagios.