To add my two cents to the conversation a process can have simultaneously open a number of sockets connected equal to this number (in Linux type sytems) /proc/sys/net/core/somaxconn
cat /proc/sys/net/core/somaxconn
This number can be modified on the fly (only by root user of course)
echo 1024 > /proc/sys/net/core/somaxconn
But entirely depends on the server process, the hardware of the machine and the network, the real number of sockets that can be connected before crashing the system