In the subject of the third mana [the third hundred] (מנה השלישית). [ note 1] The law is to leave it as long as the middleman was not negligent. [If he was, then he has to pay.] The question that come up in the gemara in Bava Metzia is why is this not divided? They answer division happens only when it could be true. [note 2] Rav Akiva Eigger askes from page 28 what about the case of signs and signs that is left. That is, there is  a lost object. two people give signs to show that it belongs to them. It is left by the finder until some absolute proof can be brought. But it could be of both so why not divide? Answers Rav Shach: division only happens when there is derara demomona [דררא דממונא] a doubt about the money and both have some prior "hazaka" ( "חזקא" holding", that is a reason to say the object is theirs.) But here the finder is not holding the object for both but only for the true owner-even if we do not know who that is.  

[I am being a bit short here because Rav Shach brings up a second question about the last mishna in the first chapter of Bava Metzia where also you leave the document even though the middleman is in fact holding the document for two people.

And I have not worked out how the argument between Sumchos and the sages fits in here--o if it is relevant at all.

[note 1] Two people give three hundred zuz  to a middleman to take care of. When they return each claims 200. If it was given together in one envelope, it stays with the middleman.

[note 2] Two people might pick up an object in the street at the same time. But the third mana belongs to one or the other, Not both.