Regarding this gemoro. After looking at it for a long time I have come to this conclusion
According the maskono. Rashi will hold that there are two things. Either the person (etsba) or the koach. If either has a chazoko she is ossur. Every person has the same 3 kochos. So if the person has a chazoko even on 3 different kochos or the three kochos have a chazoko by 3 people using all 3 she is ossur on everyone.
Tosfos learns everyone has only one koach. But not everyone the same. Apparently there are only 3 possible kochos. So if one person has 3 he is ossur. Or if 3 people have 3 then everyone is ossur.
I still havent worked out the tosfos horosh.
Mark Benson
For the moment I am just going to comment on Rashi.
1) I did not understand what you mean by "every person has the same kochos". On the contrary Rashi writes that the same person might have a different koach for every biyah.
2) Rashi does not say that if the 3 people each have a chazoka on 3 kochos that she is ossur on everyone. Rather, Rashi says that in such a case she is only permitted to the 3rd person if she does a check on the 4th biyah.
Best wishes
Dovid Bloom
Answer about Tosfos:
1) Mark, I think you were mekaven, bs'd, to the Maharam (printed below the Maharsha) who writes that it seems from Tosfos that they do not learn what is stated in the Gemara "Lefi She-Ain Kol Hakochos Shavin"; in the same way that Rashi learns it; but Tosfos learns that it means that not all people have the same kochos. However according to Tosfos each individual has the same kochos on the 3 occasions.
2) You write that if one person has 3 kochos he is ossur. But the opinion of the second paragraph of Tosfos on the page, in the name of Rabeinu Tam, is that she is always permitted with a check, even to the first husband after 3 times of seeing blood. It appears from Tosfos that even if 3 people have 3 she is still permitted with a check.
KOL TUV
Dovid Bloom
She is never ossur on anyone if she has a bedika except to people who have already seen dam with her. according to rashi. That is what I meant ossur on everyone without a bedika. I meant every person has the same 3 kochos. So if a chazaka on the kochos all are ossur.
I again meant with tosfos ossur without a bedika.
Mark, I think that we are in agreement about everything, but we must just add that what you write that each person has the same 3 kochos, only follows the opinion of Tosfos according to the Maharam.
Yasher Koach
Dovid Bloom