A person cannot perform হজ্জ on behalf of more than one person in a single হজ্জ season. হজ্জ is a complete act of worship with a unified intention (niyyah), and each performance can only be designated for one person. Just as a person cannot perform their own ওয়াজিব হজ্জ and simultaneously fulfill it for someone else, they cannot combine two proxy Hajjs into one performance.
Sheikh Ibn Baz stated clearly that each হজ্জ season, a proxy can perform হজ্জ for only one person. If someone wants to perform হজ্জ for their deceased father and mother, they would need to perform হজ্জ for one of them this year and for the other in a subsequent year. He advised prioritizing the parent who passed away first or the one with the greater right.
Sheikh Ibn Uthaymeen confirmed this ruling and added that some scholars discussed whether the general reward of a voluntary হজ্জ can be shared among multiple deceased through দোয়া and intention of gifting the reward. However, the actual হজ্জ rites — the ইহরাম, intention, talbiyah — can only be for one specific person. He distinguished between the formal proxy হজ্জ (which is specifically for one person) and general দোয়া for the deceased (which can include multiple people). A person performing হজ্জ may make dua for as many people as they wish, but the formal হজ্জ itself is for one individual only.