Yes, and this is actually the most common approach. There are three types of Haji, each handling the Umrah-Haji combination differently:
**Haji Tamattu (Enjoying):** The most sunnah type for jamaah haji coming from outside Mekkah. You enter Ihram for Umrah at the Miqat, perform Umrah in Mekkah (Tawaf, sa'i, hair cutting), then exit Ihram and enjoy normal life until the 8th of Dzulhijjah, when you enter Ihram again for Haji from your accommodation in Mekkah. This type requires an wajib animal sacrifice (hadyu). Nabi (shallallahu alaihi wa sallam) said: 'Had I known what I know now, I would not have brought a sacrificial animal and would have made it an Umrah' — encouraging Tamattu for those who did not bring animals.
**Haji Qiran (Combining):** You enter Ihram for both Haji and Umrah simultaneously at the Miqat. You remain in Ihram from the time of Umrah until after the Haji rites are completed — a significantly longer period. The Tawaf and sa'i of Umrah are combined with those of Haji. This type also requires an animal sacrifice.
**Haji Ifrad (Single):** You enter Ihram only for Haji, without performing Umrah. No animal sacrifice is required (though it is sunnah). You may perform Umrah after completing all Haji rites.
For most modern jamaah haji, Tamattu is ideal because it allows you to break from Ihram between Umrah and Haji, providing comfort during the waiting days. The sacrifice is a small price for this significant convenience.