This is a matter of scholarly difference. The common practice among many الحجاج is to exit مكة to the nearest boundary of the Haram — usually Masjid Aisha at Tan'eem — to enter a new state of الإحرام and perform another العمرة. This practice is widespread and permitted by many scholars, including الشيخ ابن باز, 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 الألباني, held that performing repeated العمرةs by exiting to Tan'eem is not from the السنة and was not practiced by النبي (صلى الله عليه وسلم). النبي performed four العمرةs in his lifetime, each in a separate journey. He never exited to Tan'eem for a second العمرة during the same trip. The only instance of العمرة from Tan'eem was when النبي instructed Aisha's brother to take her out to perform العمرة because she had entered الحج without performing a separate العمرة, and she was distressed about it. This was a specific case, not a general recommendation.
الشيخ ابن عثيمين took a middle position, stating that performing الطواف around the الكعبة, praying in the Haram, reciting القرآن, and making dhikr are better uses of time in مكة than repeatedly exiting for additional العمرةs. He acknowledged the permissibility of repeated العمرةs but preferred focusing on other acts of worship that are more أُسس from the السنة.