If I'm not thinking of the wrong AA, Ayonae's tutelage *allows* you to go higher than the 3.6 mod cap that was in place. I believe with ayonae's tutelage and the next higher one...I can't remember it atm...you can get your mod up to 4.2.
Key word in all of that is allows. It doesn't actually raise your mod, it just allows you to do so with instruments and other aa's that actually do raise your mod.