Can someone add shevu’ot on to existing shevu’ot? Can he “pile on” additional prohibitions to ones that exist already?
Issur kollel means an inclusive prohibition. In a case of issur kollel we do not find an extra prohibition added, rather the new issur expands the context of the already existing prohibition so that this activity is now included under a different category at the same time that it retains its original prohibition. An example of this is a nevelah – non-kosher meat that is forbidden in-and-of itself, that is eaten on Yom Kippur. Since Yom Kippur creates a situation wherein all food is prohibited, the nevelah will gain a second prohibition in addition to its basic prohibition.
Issur mosif means an additional prohibition. There are some cases where the issur does not fall under a larger category that adds a prohibition to it, rather there is an actual addition made to it that did not exist beforehand. One example of this is a situation where the prohibition becomes more severe, e.g. where originally there was a prohibition forbidding food to be eaten and now we find that it is also forbidden to derive any benefit from this food. Another example is where the prohibition now covers more people than it did beforehand, e.g. when someone gets married, his mother-in-law is forbidden to him, although she is permitted to the rest of the world (assuming that she is not married). Once she gets married, the prohibition no longer applies to him only, she is now forbidden to everyone in the world as a married woman.
Tosafot point out that we find some opinions that believe that in the case of issur mosif we will find one prohibition added to the existing one, but reject that same possibility in the case of issur kollel.