Answer
Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Whoever passes away while still liable for missed fast-days, regardless of whether those were originally obligatory or are due to vow, it is recommended for his guardians to make up for such missed fast days on his behalf.
2- It is permissible for a number of people to make up for the fasts on behalf of the deceased on the same day
Answering your question, The Fatwa Center at Islamweb, states:
It is permissible for a number of people to make up for the fasts on behalf of the deceased on the same day provided that such a fast does not require succession, such as the expiation of zhihar (i.e. the husband saying to his wife, “You are like my mother to me”, i.e. “You are unlawful to me exactly like my mother”) and the expiation for breaking the oath based on the scholarly view suggesting that it is obligatory to observe such fast-days successively.
Al-Hasan said,
“If thirty men fast on behalf of the deceased on the same day, it is permissible…”
Ibn Hajar wrote,
“…However, the permissibility of making up for the missed fast-days on behalf of the deceased is confined to the case in which such a fasting does not require succession given that if many persons fast on behalf of the dead person to make up for the missed days of fasting so that each one fasts a day for instance, then the element of succession is missed…” [Fath Al-Bari]
Ibn Uthaymeen advised:
“It makes no difference whether they all fast on one day or one fasts on one day and then the second fasts on the next day (and so on) until they have completed the thirty fast-days. However, in case of the expiation of zhihar and the like, the fast-days cannot be divided among the heirs because such a fasting requires succession and each of them would not observe fasting for two consecutive months as required. It is not permissible to divide the two months among more than one person; rather it is stipulated that they should be fasted by one person so that it can truly be said that he fasted two consecutive months. One may ask if it is acceptable that one of the heirs could observe fasting for three days in succession and then abstain from fasting and another one observes fasting for another three days and so on. In fact, this is not acceptable because it could not truly be said that any of them fasted two consecutive months as required. Hence, if the deceased was obliged to fast for two consecutive months, then either one of his heirs volunteers to fast them on his behalf, or rather they may feed one poor person for each day.”
Allah Almighty knows best.