What is the ruling on supplicating after the obligatory prayer, and is there any evidence to prohibit that?

Raising the hands in supplication after the obligatory prayer was not preserved from the Prophet (peace and blessings be upon him) nor from his Companions, and therefore it is considered an innovation (bid'ah). As for supplicating without raising the hands collectively, there is no harm in it, and similarly, supplicating after the supererogatory prayer, even with raising the hands sometimes; because raising the hands is one of the means of acceptance. However, this should not be done on a permanent basis, and goodness lies in emulating the Prophet (peace and blessings be upon him).