Is it a condition that each person takes their share from their own sacrifice, or can the shares from several sacrifices be collected and distributed among the participants, and then the remainder be distributed to the poor?

It is permissible to share in a sacrifice if it is a camel or a cow, as seven people may share in one of them, just as the Companions did with the Prophet, peace and blessings be upon him. It is sunnah (definition) to eat from the sacrifice, give some in charity, and give some as a gift, and this is the view of the majority of jurists. If it is not possible to slaughter all the sacrifices on the day of Eid, then what is feasible can be slaughtered on the first day, and everyone takes their share of the meat. Then the rest can be slaughtered on the following day, keeping in mind that a portion from each cow should be given in charity, and the owners of the sacrifice should be designated at the time of slaughter.