How many TCP/IP socket connections can a system(computer) handle?

How many TCP/IP socket connections can a system(computer) handle?

I have been working on a project regarding TCP/IP socket connection and
message transferring through these sockets. I am connecting to a UNIX
server with a specific IP address and establishing socket connections. So
far I could manage roughly 16000 connections from 1 host (in this case
this is my own pc). And when I try establishing other connections from
other hosts (either it is Mac Osx or Windows PC), I reached the same
maximum connection number, 16000.
I can have 65536 connections on server side and I literally maintained
that. But only when it is 16000 connections in each of 4 different
computers. I wonder why I have this and how I can establish more than
16000 connections from only 1 host.