Yes, and this is actually the most common approach. There are three types of হজ্জ, each handling the উমরাহ-হজ্জ combination differently:
**হজ্জ Tamattu (Enjoying):** The most মুস্তাহাব type for হাজীগণ coming from outside মক্কা মুকাররমা. You enter ইহরাম for উমরাহ at the Miqat, perform উমরাহ in মক্কা মুকাররমা (তাওয়াফ, সাঈ, hair cutting), then exit ইহরাম and enjoy normal life until the 8th of Dhul Hijjah, when you enter ইহরাম again for হজ্জ from your accommodation in মক্কা মুকাররমা. This type requires an ওয়াজিব animal sacrifice (hady). নবী করীম (সাল্লাল্লাহু আলাইহি ওয়া সাল্লাম) said: 'Had I known what I know now, I would not have brought a sacrificial animal and would have made it an উমরাহ' — encouraging Tamattu for those who did not bring animals.
**হজ্জ Qiran (Combining):** You enter ইহরাম for both হজ্জ and উমরাহ simultaneously at the Miqat. You remain in ইহরাম from the time of উমরাহ until after the হজ্জ rites are completed — a significantly longer period. The তাওয়াফ and সাঈ of উমরাহ are combined with those of হজ্জ. This type also requires an animal sacrifice.
**হজ্জ Ifrad (Single):** You enter ইহরাম only for হজ্জ, without performing উমরাহ. No animal sacrifice is required (though it is মুস্তাহাব). You may perform উমরাহ after completing all হজ্জ rites.
For most modern হাজীগণ, Tamattu is ideal because it allows you to break from ইহরাম between উমরাহ and হজ্জ, providing comfort during the waiting days. The sacrifice is a small price for this significant convenience.