Is it permissible for a person to make supplication in each sajdah of an obligatory prayer?

It is permissible for a person, whether praying individually or in congregation, to make supplications during sujud [prostration] in both obligatory or voluntary prayers. However, it is disliked for the imam to do so since he is required to spare the congregation any sort of hardship, unless he is leading a certain group who do not mind lengthy prayers.
And God the Almighty knows best.