Limiting simultaneous connections

Is there a way to limit the number of simultaneous connections that any
given username can make to the database? For instance, I'd like user1 to be
able to have no more than 5 simultaneous connections to the database server,
but user2 can have 15 simultaneous connections.

Also, can these connections be limited on a per user for the entire database
server basis? Or can they be limited on a per user per database basis? By
this I mean, can a user create up to 5 connections to one of their databases
and then another 5 to one of their other databases (total of 10 connections
across the whole database server). Or can they be limited to a total of 5
for any connections to any of their databases?

I will be using either 7.1.1 from RPM or 7.1.2 from source on Red Hat Linux
6.2 and 7.1.

Thanks!
Tauren