An IP can only issue most 65536 connections to a server, since socket port is unsigned short. But we can bypass this limit. On Linux, it’s quite easy to set up virtual network interface:
for i in `seq 200 230`; do sudo ifconfig eth0:$i 192.168.1.$i up ; done
Then your computer have many IPs, from 192.168.1.200 to 192.168.1.230. The server bind to 0.0.0.0@port, the client can connect 192.168.1.200@port, or 192.168.1.201@port, etc. Per IP can have about 60K concurrent connections. Then the client can issue as many concurrent connections as it needed.