I wouldn't just go in and bump max connections, increasing this value too high will cause your server to start swapping due to the memory requires *each* client requires.
I have worked on domains that are doing 50 qps where the person did the same thing and brought his entire domain to a halt, and if you properly tune all of your queries you can live with 128 connections without a single issue. After tuning it was doing 100~150 qps.
What I would recommend is setting thread_cache_size to 100, this will reduce a significant amount of system CPU time due to creation/destruction of threads -- which ultimately slows down how many connections can come & go because they have to wait for their thread to be created.
In general I would suspect your issue is related to the queries not having proper indexes, or simply the wrong queries (cartesian products, improper schema design, etc).
I have worked on quite a few servers and rarely found max_connections to be a solution, but more of a problem. As the end result is thrashing due to excessive swapping.