There is a very fundamental argument between the Rashba and Ran in how we learn out the concept of נותן טעם לפגם (bad flavor) being permitted. The gemara speaks about נותן טעם לפגם being permitted to eat in two ways: 1. An item that is essentially fit to eat, but gives an off flavor either because it is slightly spoiled or because it doesn't compliment the food that it fell into (see rashi 67a d.h. kol, that this category doesn't need to be not eatable). 2. The issur deteriorates to such a degree where it is no longer fit to eat.
Tosafos 67a elaborates in their rejection of Rashi in Chulin 98b who holds that the concept of ta'am k'ikar is only Rabbinic which means that the application of the heter of נותן טעם לפגם to giving an off flavor (#1 above) only needs to be a rabbinic heter. Tosafos proves that we hold the concept of ta'am k'ikar to be d'oraysa and discusses the possibility of being able to give malkus for just ta'am of issur because it is literally like the issur itself. According to this approach, the heter of נותן טעם לפגם that permits the taste of issur even when it is just slightly off, would need to be דאורייתא.
The Rashba and Ran disagree about the source for the first type of נותן טעם לפגם. The Rashba writes that the gezeiras ha'kasuv of ta'am k'ikar which is the source that taste alone is considered significant like the item itself, only applies to a positive taste but not to a negative taste. The Ran (32b in Rif) points to the gemara 67b that asks for the source of נותן טעם לפגם and darshens the pasuk of לא תאכלו כל נבלה לגר אשר בשעריך - כל הראויה לגר קרויה נבלה, שאין ראויה לגר אינה קרויה נבלה. This pasuk teaches that any issur which is not fit for human consumption doesn't qualify as issur, and somehow uses this as the source to permit all נותן טעם לפגם even when the item is still fit to eat. The Ran explains the connection: Just as neveila which is spoiled and unfit to eat is permitted because the eater no longer enjoys or benefits from it, so too when an issur food gives a bad flavor to the soup that it fell into, the taste is permitted since the eater doesn't benefit from the issur. Therefore, the Ran writes that when the issur increases the quantity to a point where the benefit of the increased quantity offsets the minor detriment caused by the off flavor, the food would be forbidden (unless it literally deteriorates until it is no longer fit to eat at all).
There seems to be a fundamental argument between the Rashba and Ran in the nature of the heter of נותן טעם לפגם. The Rashba holds that there is no inherent relationship between the two categories of נותן טעם לפגם that were mentioned above. A food which is unfit to eat the Torah considers like dust from the drasha of שאין ראויה לגר אינה קרויה נבלה. But, when the issur is eatable just gives an off flavor, it retains it's status of issur, but the flavor it contributes to the soup is not included in the prohibition of ta'am k'ikar (the pri megadim explains that the gemara doesn't mean to learn the source of נותן טעם לפגם from neveila, just the premise of p'gam being mutar). However, the Ran holds that there is an inherent connection between these two categories. The entire heter of ne'veila that spoils is not because it is considered dust, rather because the Torah only forbids issur when there is hana'ah (benefit and enjoyment) from the eating of it. So long as there is no benefit or enjoyment it is permitted, therefore even when the issur is still eatable but contributes an off flavor it will not assur the soup. In short, the Rashba holds that the heter of neveila that is not eatable is a heter on the cheftzah and cannot be applied to an eatable food that gives off a bad flavor. But, the Ran holds that the heter of ne'veila is a heter on the gavra because he is not benefiting from the issur, which also applies to a case where eatable issur puts a bad flavor into the soup - but wouldn't apply when there is a benefit from the increased quantity.
The (pri megadin y.d. 103 m.z. 1) explains that according to the Rashba that the nature of נותן טעם לפגם is that it isn't included in ta'am k'ikar, we would still require bitul b'rov to permit the small amount of issur that is present (just that it won't assur up to 60x since it isn't included in the chiddush of ta'am k'ikar). But according to the Ran, so long as the person isn't benefiting from the issur being there, it is permitted to eat, no bitul is necessary. Therefore, the pri megadim suggests that they go li'shitasam regarding the machlokes whether on pesach we can permit נותן טעם לפגם. The Rashba holds that the heter of נותן טעם לפגם requires bitul, and since by chometz we are machmir for even the smallest amount (ma'shehu), we can't apply the heter of נותן טעם לפגם. But, the Ran who holds that נותן טעם לפגם wouldn't require bitul would apply the heter of נותן טעם לפגם even to chometz on pesach.
See the chazon ish (y.d. 30:2) for a more detailed discussion of the Ran, and whether the Ran would permit even when a 5 cups of issur falls into 4 cups of heter but spoils the flavor of the heter to a point where the increased quantity is not beneficial, or would the Ran still require that the quantity of heter be greater than the issur.
The Shulchan Aruch (Y.D. 103:2) is machmir (ויש מי שחוכך לומר) for the Ran when there is benefit from the increased quantity and the rama seems to agree, yet the rama in o.c. is also machmir for the Rashba (Shulchan Aruch O.C. Hilchos Pesach 447:10) that נותן טעם לפגם is assur because it requires bitul.