This is a matter of scholarly difference. The common practice among many حجاج is to exit مکہ مکرمہ to the nearest boundary of the Haram — usually Masjid Aisha at Tan'eem — to enter a new state of احرام and perform another عمرہ. 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 عمرہs by exiting to Tan'eem is not from the Sunnah and was not practiced by نبی کریم (صلی اللہ علیہ وسلم). نبی کریم performed four عمرہs in his lifetime, each in a separate journey. He never exited to Tan'eem for a second عمرہ during the same trip. The only instance of عمرہ from Tan'eem was when نبی کریم instructed Aisha's brother to take her out to perform عمرہ because she had entered حج without performing a separate عمرہ, 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 طواف around the کعبۃ اللہ, praying in the Haram, reciting قرآن, and making dhikr are better uses of time in مکہ مکرمہ than repeatedly exiting for additional عمرہs. He acknowledged the permissibility of repeated عمرہs but preferred focusing on other acts of worship that are more established from the Sunnah.