This is a topic where the schools of jurisprudence have different positions. The Shafi'i and Hanbali schools permit performing multiple উমরাহs in one trip, citing the hadith where নবী করীম (সাল্লাল্লাহু আলাইহি ওয়া সাল্লাম) instructed Aisha's brother Abdur-Rahman to take her to Taneem to enter ইহরাম for a second উমরাহ during the Farewell হজ্জ. The Hanafi school generally permits it as well.
The Maliki school and scholars like Ibn Taymiyyah consider performing multiple উমরাহs in one trip to be disliked (makruh). Their reasoning is that the companions of নবী করীম, despite living in or frequently visiting মক্কা মুকাররমা, did not repeatedly perform উমরাহ. They advise that voluntary তাওয়াফ around the কাবা শরীফ is more meritorious for someone already in মক্কা মুকাররমা than going out to Taneem to re-enter for another উমরাহ.
If you choose to perform a second উমরাহ, the process is: exit the Haram boundaries to the nearest Miqat point for মক্কা মুকাররমা residents, which is Masjid Aisha (also called Masjid Taneem), approximately 7 km from the Haram. Enter ইহরাম there with the intention for উমরাহ, then return to the Haram and perform the complete উমরাহ rites (তাওয়াফ, সাঈ, and hair cutting/shaving). There is no fixed waiting period between উমরাহs. Many হাজীগণ perform a second উমরাহ on behalf of a deceased relative or someone unable to perform it themselves.