Firstly: 

It is permissible to share in a sacrifice if it is a camel or a cow. 

It is permissible for seven people to share in one sacrifice of a cow or a camel. 

It is proven that the Sahaabah (may Allah be pleased with them) shared in sacrifices (hadiy), seven sharing a camel or a cow, in Hajj and ‘Umrah. 

Muslim (1318) narrated that Jaabir ibn ‘Abd-Allah (may Allah be pleased with him) said: In the year of al-Hudaybiyah we offered the sacrifice with the Messenger of Allaah (blessings and peace of Allah be upon him), a camel on behalf of seven and a cow on behalf of seven. 

According to another report: We set out with the Messenger of Allaah (blessings and peace of Allah be upon him) entering ihraam for Hajj, and the Messenger of Allaah (blessings and peace of Allah be upon him) told us to share (in sacrificing) camels and cattle, every seven of us sharing an animal. 

For more information, please see the answer to question no. 45757. 

Secondly: 

It is Sunnah to eat from the sacrifice but it is not obligatory according to the majority of fuqaha’. 

In Zaad al-Mustaqni‘ it says: It is Sunnah to eat one third, give one third as gifts, and give one third in charity. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said in his commentary: The words “It is Sunnah to eat one third, give one third as gifts, and give one third in charity” mean it is prescribed, not in the sense that it is obligatory, but that it is mustahabb to divide it into thirds and eat one third, give one third as gifts, and give one third in charity. 

The difference between gifts and charity is that what is given as an act of friendship is a gift, because of what it says in the hadeeth, “Give one another gifts and you will love one another.” And what is given so as to draw close to Allah is charity. Based on this, charity is given to one who is in need and a gift is given to one who is independent of means. 

Dividing it into thirds, i.e., one third for eating, one third for giving as gifts and one third for giving in charity, is done so that people of all classes or levels will benefit from his sacrifice. Eating it oneself is mentioned first because Allah mentioned it first in the verse in which He said (interpretation of the meaning): “Then eat thereof and feed therewith the poor having a hard time” [al-Hajj 22:28]. 

With regard to the words “It is Sunnah to eat”, the apparent meaning is that if he gives all of it in charity, there is nothing wrong with that and he is not sinning. This is based on the fact that eating from one’s sacrifice is Sunnah, as is the view of the majority of scholars. 

Some of the scholars said: Rather eating from it is obligatory and he is sinning if he does not do that, because Allah has enjoined it and given it precedence over charity; and because the Prophet (blessings and peace of Allah be upon him), during the Farewell Pilgrimage, enjoined that a piece be taken from each sacrificial animal and placed in a pot and cooked, then he ate some of its meat and drank some of its broth. They said: To go to the effort of taking one hundred pieces from one hundred camels and cooking them in a pot and eating from that indicates that the command in the verse is given in the sense of it being obligatory. And because this comes under the heading of enjoying the blessings of Allah, so it is included in the words of the Prophet (blessings and peace of Allah be upon him): “The days of al-Tashreeq (the 11^th, 12^th and 13^th of Dhu’l-Hijjah) are days of eating, drinking and remembering Allah, may He be glorified and exalted.” 

Whatever the case, the individual should not refrain from eating from his sacrifice. 

End quote from al-Sharh al-Mumti‘, 7/481 

If the matter is as you described, and it will be difficult to slaughter seven cows in one day, and everyone wants to take meat on the same day, there is nothing wrong with that. So you should slaughter as many as you can, then everyone should take some of the meat. For those whose cow could not be slaughtered on the first day, they may take some of the meat, even if it is only a little, when it is slaughtered on the second day. But you should pay attention to two matters: 

1.It is essential to set aside some of the meat of each cow for charity and it should not all be distributed to those who are offering the sacrifice, whether it is slaughtered on the first day or after that.

2.It is essential to specify who has shared in the sacrifice at the time of slaughter, so it should be intended that this cow is offered on behalf of So and so, mentioning each of them by name. It is not sufficient to slaughter all the cows on behalf of all the participants; rather it is essential to identify exactly on whose behalf each cow is being sacrificed.

And Allah knows best.