Is it permissible to perform supererogatory prayers (nawafil), such as the regular Sunnah prayers and others, while making up missed obligatory prayers (fawait) according to the Shafi'i and Hanafi schools of thought?

The jurists differed regarding making up missed regular Sunnah prayers. The Hanafis are of the view that only the Fajr Sunnah prayer should be made up, while the Shafi'is recommend making up all regular supererogatory prayers, according to the soundest opinion within their school. The Malikis, Abu Hanifa, and Abu Yusuf, in the most famous narrations, held the view that they should not be made up. One must prioritize making up missed obligatory prayers first if there is a concern that they will be missed due to making up Sunnah prayers.