Giving a detailed explanation on this issue, Dr. `Abdel-Fattah Idrees says:

“It is permissible to perform more than one Umrah in the same visit, for it has been reported that the Companions of the Prophet (peace and blessings be upon him) performed more than one umrah in the same visit.

Also, there is a repot that Anas Ibn Malik (may Allah be please with him) used to perform umrah whenever the hair of his head germinated. Hence, as hair continually germinates and never stops growing, we can assume that Anas performed umrah every week or every ten days. It has even been reported that one of the Companions whenever he travelled to Mecca, he performed umrah every month. These are evidences for repeating umrah in the same visit.

In view of the above explanation, there is no considerable evidences to prevent doing this.  Therefore, the basic rule is to let the absolute injunction remain absolute in meaning until there comes a qualifying evidence.”