Mishnah 8 in chapter 3 of Maseches Challah deals with leaven that became mixed into dough that is exempt from challah: a person took leaven (a sourdough starter) from dough from which challah had not been separated, and mixed it into dough from which challah had already been separated. The result is that the leaven is obligated in challah, while the dough it was mixed into is already exempt. The question is what the correct way is to separate challah for that leaven.
The first explanation - "sipuk mimakom acher" from another batch of dough:
When he has another batch of dough that is obligated in challah, he may separate only against the measure of the leaven that is in the mixture. Suppose the leaven makes up one twenty-fifth of the mixture: he takes from that other source an amount equal to the measure of the leaven alone, and separates challah from it.
The novelty of the Mishnah - "ta'am ke'ikar":
One might have thought that the leaven mixed into the dough is nullified, as though it does not exist at all; and if so, one who takes challah from another dough that is obligated in challah on behalf of the leaven would be separating from what is obligated on behalf of what is exempt. The Mishnah teaches that the leaven is not nullified, since "ta'am ke'ikar" - flavor has the status of the substance itself - applies by Torah law: the flavor that the leaven imparts to the dough is considered as though the leaven is actually present, and this is so even on the Torah level. Therefore there is a genuine obligation of challah here on account of the leaven, and so separating from another dough that is obligated in challah is effective for it.
An additional explanation - adding flour:
Other commentators explain "sipuk mimakom acher" differently: if he has additional flour, he may add it to the mixture in which the leaven that is obligated in challah is found (since the rest of the dough there is not obligated). He adds an amount of flour that will combine together with the leaven to make up the measure of challah on its own, and then he separates challah only against that amount - the obligation that takes effect on the combination of the flour he added together with the leaven.
When there is no supply from another source:
The Mishnah concludes: if he has neither another dough that is obligated in challah nor additional flour - "motzi challah achas al hakol" - he takes out one challah for the whole batch. That is, he must separate the standard measure of challah from the entire dough, and not only against the leaven that was mixed into it, as though all of the dough were obligated in challah.
In summary: In this Mishnah we learned the law of leaven that is obligated in challah which became mixed into dough that is exempt. If he has a supply from another source - whether another dough that is obligated in challah or additional flour that he will add to the mixture - he separates only against the measure of the leaven; and if he does not, he takes out one challah for the whole batch. The novelty of the Mishnah is that the leaven is not nullified in the mixture, since "ta'am ke'ikar" applies by Torah law, and therefore a full obligation of challah takes effect here.