The Gem. cannot seem to find an animal that an 'Ir Hanidachas' might bring (to be unique) because all the different chosen animals are already used for other Korbonos.
That is true!-but couldn't 'Ir Hanidachas' have been made unique by changing the number of animals to have been brought?
We do see other cases of 2 animals being brought. So we just pick a different 2 animals that were never used!
Kol Tuv
alex lebovits, toronto, canada
A similar question to yours is asked by Tosfos DH Mai, that the Ir ha'Nidachas should bring a sheep or a ram. The Tosfos Rosh answers this question by asserting that we cannot invent a new "Chatas" sacrifice that we never found anywhere else. Tosfos Rosh in Horayos 8a states this slightly more clearly by writing that "it is obvious to the Talmud that we should not invent a new sacrifice from which one never gets atonement from for a transgression" (see also the Ritva).
Therefore it seems that just as we cannot invent a new species as a Korban, so also we cannot make up new combinations of 2 existing Korbanos. However the Gemara did conclude that one might have thought that since we found, when the Beis Din ruled that idol worship is permitted and the community followed this, that they subsequently bring a cow for an "Olah" and a goat for a Chatos, therefore the Ir ha'Nidachas might have brought a cow for a Chatas and a goat for an Olah. However that means taking an existing combination and merely switching round what purpose each animal is brought for, but it seems that to make up a totally new combination, clearly was not a possibility (see Ritva).
KOL TUV
D. Bloom