One domain, one external IP, two ports, one machine, three servers

Question

I have one raspberry pi, running an Apache2 webserver on port 80, an Ogar (Agario) server running on port 443 and another Ogar server on port 444. The external location that I need to access this website from, however, only allows connections from two ports (80, 443). I have one domain. How can I merge port 443 and 444, so I can do something such as

example.com:80 (web)
example.com:443/server1
example.com:443/server2 (actually port 444)