All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is permissible for anyone who comes to Makkah for the Umrah to perform more than one Umrah on the same journey, be it for himself or one behalf of his ill father who is unable to perform Umrah on his own and whose illness is incurable. This is of course after having performed Umrah for himself. Not only that, but repeating Umrah is amongst the virtuous deeds. The Messenger of Allah (Peace and blessings be upon him) said: "(The performance of) 'Umrah is an expiation for the sins committed between it and the previous 'Umrah; and the reward of Hajj Mabrur (i.e., one accepted) is nothing but Jannah." [Muslim].
However, he must start his second Umrah from a point outside the Haram area. The nearest is the mosque at Taneem. During the farewell pilgrimage, Ayisha (May Allah be pleased with her) performed two Umrahs in twenty days. One when she entered from Madinah and one where the Prophet (Blessings and peace be upon him) ordered her to start from Taneem.
Narrated 'Aishah:
The Prophet (Blessings and peace be upon him) sent my brother, 'Abdur Rahman with me to Tan'im for the 'Umra, and he made me ride on the packsaddle (of a camel). Umar said: "Be ready to travel for Hajj as it (Hajj) is one of the two kind of Jihad" {Bukhari & Muslim}. An-Nawawi (May Allah have mercy on him) said: "If the person who comes to Makka for Umrah is a resident of Makkah or is passing through, then his Miqat (The principal boundary at which a Muslim pilgrim intending to perform the Haj or the Umrah must enter into the state of Ihram) is Al-Hil (The area between the boundaries of the Mawaqit and the boundary of the Haram." This is as stated by Al-Shafie and agreed upon by his fellow scholars. The latter stated: "It suffices that he takes one foot inside the Hil area from any side for this is the obligatory Miqat. As for what is recommended in this regard, Al-Shafie mentioned in his book [Al-Mokhtasar]: "It is recommended that he enters into the state of Ihram for Umrah from Al-Jo`ranah, because the Prophet (Blessings and peace be upon him) did so or from Tan`im because he (Blessings and peace be upon him) sent Aisha there for Umrah or from Al-Hudaibeyiah because he (Blessings and peace be upon him) prayed there. However, it is better to enter into the state of Ihram for Umrah from Al-Jo`ranah, then Tan`im, then Al-Hudaybiah." [Al-Majmou`, vol.7/pp.211}. Also kindly check {Moghni Al-Mohtajj, vol.2/pp.229}.
Ibn Qhoddamah even stated that there is no disagreement between scholars on the permissibility of the Umrah of the one who comes to Makka or is already one of its residents. He said: "Makkah is the Miqat for Haj to whoever is it, but if he wants to perform Umrah, then he has to go to Al-Hil, and there is no disagreement on this amongst the scholars and this is why the Prophet (Blessings and peace be upon him) ordered AbdulRahman to take Aisha to Tan`im to start her Ihram for Umrah. {Al-Moghni, vol.3/pp.11}.
In conclusion, it is permissible for anyone who comes to Makkah for the Umrah to perform more than one Umrah on the same journey as long as there is no text (Quran & Sunnah) forbidding that. Moreover, scholars in general have deemed this permissible. And Allah The Almighty Knows Best.