There's no known POST call limit I'm aware of on our cPanel hosting. To be honest there is likely a lot more unknown variables were not aware of that's causing this error to occur when more than one user is logged in.
One thing you may want to try is reviewing your error logs to see if there's any more details that come up that might help lead to a solution. Beyond that, you're always welcome to reach out to our live support so our hosting team can help review the matter with you within your hosting account.
CG - GoDaddy | Community Moderator 24/7 support available at x.co/247support