I think what you are talking about is campaign tracking. You’d have your link code look something like: w w w .SITE.com/?accountid=XXX&promoid=yyy. No need to signup for multiple affiliate accounts. I imagine most programs offer this (gamblegains does! 
).
It’s the most flexible way to give affiliates the opportunity to control their stats – also it’s the most time consuming since you’d have to set a new campaign for every ad you use (to track which sale came from which banner).
Just poke around some of the programs you are currently promoting, I’d be shocked if most didn’t have this option tucked away somewhere.