When using screen -x NAME is there a max number of connections to a single screen?
The maximum number of users logged in on a Linux system is limited by the number of available pseudo terminals. The maximum number of these is found in
/proc/sys/kernel/pty/max (4096 on my test machine).
This would be an upper limit to how many users would be able to give the
screen -x command.
On non-Linux systems, the limit would also be set by the maximum number of allowed concurrent users. On NetBSD and OpenBSD, pseudo terminals may be created up to a limit of 992.