Every Heart Scale lets you have 1 'move rememberance', and you can get endless Heart Scales, right (you can hold 999 at a time, though)? So then you can get endless move rememberances, so long as you have a Heart Scale.
In other words, as many as you would like, so long as you have a Heart Scale.
You can get easy Heart Scales daily with a girl in Drifveil City, just talk to her and teach a Pokemon the move she'd like to see, and talk to her again once you've taught a Pokemon in your party the move. Se will give you a Heart Scale, but only one a day.
