Zevachim 76 - A Leniency That Leads to a Stringency
If a guilt-offering became intermingled with a peace offering, then we have a problem that the guilt-offering bears more limitations, even though their blood services are equivalent. Rabbi Shimon suggests that we can still resolve the situation by bringing both in the north (which will work for both types of sacrifices) and eating them according to the stringencies of the guilt-offering. We will have brought the offerings right away.
However, the Sages disagree with this solution because of the principle that one may not expose offerings to more invalidations than necessary. By applying the stringencies of a guilt-offering to both, one shortens the time to eat the peace offering, which may lead to its invalidation. Rather, the animals to be offered should be left to graze until they become blemished, then sold, and the money from the proceeds should be used to buy replacement offerings.
Where pieces of meat of different offerings became intermingled, everybody agrees that they have be eaten with the limitations of the most stringent of them - since in this case there is no way out similar to the above.
Art: Heinrich Bürkel - The Village Cattle Market