A person cannot perform الحج on behalf of more than one person in a single الحج season. الحج 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 واجب الحج and simultaneously fulfill it for someone else, they cannot combine two proxy Hajjs into one performance.
الشيخ ابن باز stated clearly that each الحج season, a proxy can perform الحج for only one person. If someone wants to perform الحج for their deceased father and mother, they would need to perform الحج 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.
الشيخ ابن عثيمين confirmed this ruling and added that some scholars discussed whether the general reward of a voluntary الحج can be shared among multiple deceased through الدعاء and intention of gifting the reward. However, the actual الحج rites — the الإحرام, intention, talbiyah — can only be for one specific person. He distinguished between the formal proxy الحج (which is specifically for one person) and general الدعاء for the deceased (which can include multiple people). A person performing الحج may make دعاء for as many people as they wish, but the formal الحج itself is for one individual only.