Is it permissible to make up the pre-noon prayer (four rak'ahs) after the obligatory prayer, and then perform the post-noon prayer (two rak'ahs)?

According to the Shafi'is, and it is well-known among the Hanbalis, it is recommended to make up missed supererogatory (Sunnah Rawatib) prayers, based on the Hadith of Umm Salamah that the Prophet, peace and blessings be upon him, prayed two rak'ahs after 'Asr, which he had been preoccupied from performing earlier. As for the manner of making them up, if one missed the pre-Dhuhr Sunnah and wishes to make it up after the obligatory Dhuhr prayer, one should first pray the post-Dhuhr Sunnah and then make up the pre-Dhuhr Sunnah.