Can more than 7 People Share in the Qurbani of a Single Cow?

Assalamu Alaikum wa Rahmatullah, I understand that a cow can be divided among up to 7 people. But what if a large extended family wants to participate and mentions more than 7 names? If some of those named are children or elders who are financially dependent, and not paying for a share, is it still valid? Is the rule about 7 people based on names or financial shares? I want to ensure our Qurbani is valid and not done incorrectly. Answer from Qur'an and Authentic Sunnah and what Salaf-e-Saliheen used to do. Jazakum Allahu Khairan.