This is a matter of scholarly difference. The common practice among many pilgrims is to exit Makkah to the nearest boundary of the Haram — usually Masjid Aisha at Tan'eem — to enter a new state of ihram and perform another Umrah. This practice is widespread and permitted by many scholars, including Sheikh Ibn Baz, who considered it a virtuous deed and a form of drawing closer to Allah.
However, a number of scholars, including Sheikh al-Islam Ibn Taymiyyah and Sheikh Al-Albani, held that performing repeated Umrahs by exiting to Tan'eem is not from the Sunnah and was not practiced by the Prophet (peace be upon him). The Prophet performed four Umrahs in his lifetime, each in a separate journey. He never exited to Tan'eem for a second Umrah during the same trip. The only instance of Umrah from Tan'eem was when the Prophet instructed Aisha's brother to take her out to perform Umrah because she had entered Hajj without performing a separate Umrah, and she was distressed about it. This was a specific case, not a general recommendation.
Sheikh Ibn Uthaymeen took a middle position, stating that performing Tawaf around the Ka'bah, praying in the Haram, reciting Quran, and making dhikr are better uses of time in Makkah than repeatedly exiting for additional Umrahs. He acknowledged the permissibility of repeated Umrahs but preferred focusing on other acts of worship that are more established from the Sunnah.