One of the things I really like about Push is that the pads allow the use of aftertouch. There two new and free Max for Live devices by Subaqueous that enhance the use of aftertouch on Push.
(aq) Aftertouch - Threshold
With this effect, the aftertouch is only applied over a set threshold for the pressure on the pads of Ableton Push. You can map the aftertouch to your desired parameter and there's also an added smoothing effect.
(aq) Aftertouch - Delay
This one is very similar, but instead of a threshold the aftertouch can be delayed by a set amount of milliseconds. It was created with filters in mind and thus also sports an attack and release value.