1)    The law of praying a supplementary prayer when one erred and did not pray correctly applies only when the reason that he did not pray was because of a mistake or because he was forced not to pray. It also applies if he was drunk or ill at that at time. It applies even to one who did not pray because his mind was unsettled (even though he acted unlawfully and really should have prayed) as he is still not considered as having deliberately not prayed. All of the above people may pray a supplementary prayer to make up for the one that they missed. (Shulchan Aruch and Mishne Berurah 108)

2)    However, one who deliberately did not pray, may not make up with a supplementary prayer. However, he may pray a voluntary prayer. When doing this there are some halachic authorities who maintain that he must invent in it a new request which he had not requested in his main prayer (ideally he should add something new in each of the middle blessings, but nevertheless in the event that he only added something in one of the blessings that suffices). However, on Shabbos one may not pray a voluntary prayer. (ibid)