Repeated Entering into Iḥrām for ʿUmrah

Answer—and Allah grants success: What is superior for one who has reached Makkah and wishes to perform voluntary worship after his Hajj and after his ʿUmrah is to perform voluntary ṭawāf of the House, and to pray two rakʿahs after every seven circuits, and to repeat that as much as he wishes. It has come from the Prophet (May Allah bless him and his family and grant them peace)—in meaning—that ʿUmrah is ṭawāf of the House.
What we have mentioned is most likely what is legislated. Before his mission and after it, when the Prophet (May Allah bless him and his family and grant them peace) entered al-Masjid al-Ḥarām, he began with ṭawāf of the House, as is mentioned in the books of sīrah. This is what the early generations used to do, as it appears.
As for what is mentioned in the question, it has not been transmitted that the Prophet (May Allah bless him and his family and grant them peace) did it, nor the Muslims after him.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.1