Praise be to Allah.
This is permissible, but it is not Sunnah. The Sunnah is for a person not to repeat ‘Umrah during the one trip, rather it is sufficient to perform the ritual once, because that is what the Prophet (peace and blessings of Allaah be upon him) did. With regard to the person on whose behalf you want to do ‘Umrah, it is better to pray for him. That is the best thing to do in this case.