Based on Google Analytics real time report I can serve around 450+ concurrent sessions using our UpCloud.com 6-core / 16GB RAM VPS. They have one of the fastest servers around. But this is obviously a guesstimate, as GAnalytics is not the most accurate way to measure this, and the number of user activity (participating / logged in / guest) varies case by case.
We have this busy day only once a year and always the hickups have started to occur somewhere around the 450 sessions marker on GAnalytics. If the site starts to choke the number of sessions naturally drops rapidly.