Praise be to Allah.
It is permissible for the pilgrim doing tamattu‘, who has completed his ‘Umrah and is staying in Makkah waiting for Hajj, to do ‘Umrah during this period, especially if he leaves Makkah to go to Madeenah and the like, then comes back to Makkah. And that does not mean that he has to offer more than one sacrifice, because what is meant in the verse is that the one who does Hajj tamattu‘ has to offer a sacrifice. Even if he does ‘Umrah repeatedly, he is not going to do Hajj more than once, so he does not have to offer any more than one sacrifice.
But is it prescribed for one who is staying in Makkah and not leaving to repeat ‘Umrah as many people do nowadays, by going out to at-Tan‘eem to enter ihram for ‘Umrah?
There is a difference of opinion concerning that among the scholars. Some of them say that there is a concession allowing that, and others say that it is makrooh and regard it as being contrary to the actions of the salaf (early generations).
And Allah knows best.