The ruling on offering separate sacrifices for different family members and performing more than one sacrifice

It is also permissible to offer a separate sacrifice on behalf of family members. The evidence for this is the following hadith. Sayyida Aisha (may Allah be pleased with her) narrates:

وضحى رسول الله صلى الله عليه وسلم عن نسائه بالبقر

“The Messenger of Allah (peace be upon him) sacrificed a cow on behalf of his wives (during the Farewell Pilgrimage).”

Offering more than one animal as a sacrifice is a Sunnah and recommended act, provided that in this act there is adherence to Sunnah, sincerity, attainment of piety, and devotion to Allah.
Sayyiduna Anas bin Malik (may Allah be pleased with him) narrates:

كان النبى صلى الله عليه وسلم يضحي بكبشين وأنا أضحي بکبیشن

The Prophet (peace be upon him) used to slaughter two rams, and I also slaughter two rams.

Benefit:

Ibn Battal, may Allah have mercy on him, states:

فمن أراد أن يضحي عن نفسه باثنين أو ثلاثة، فهو أزيد فى أجره إذا أراد بذلك وجه الله وإطعام المساكين

“The person who wishes to offer two or three sacrifices on his own initiative, this act brings him greater reward and merit, provided that the purpose of this act is the pleasure of Allah and feeding the poor.”