A character isent defined by his classes. I think the issue is that your not seeing the game beyond stereo type. Classes create stereo types. A fighter will always be a fighter no matter what he does or how he acts. A dm that cant see past the classes i have found treat classes a curtain way. When someone heavily multi classes to archive a concept, some dms and players do not know how to react to that. They don't know what that character is, and see it as a mess. But most of the time, this is because they cannot look beyond the classes system for a way to define the character itself. They think it needs a name like fighter or wizard, when people in real life tend not to fall into such broad generalizations. Why should characters?
I think the benefit of multi classes is you can make a character thats a warrior that could have a back story were he fights spell casters but given the right combo of feats and classes, he could actually show that he is proficient at it when he encounters spell casters. Nothing is more humiliating then saying your X in your back story and being mocked later when the mechanics cannot represent this.
take my favorite martial combo, monk2, fighter2, barbarian2. This combination is a much stronger idea of what I think a well rounded warrior is, compared to just a fighter, or just a monk, or just a barbarian. The back story potential, in turn is in turn offers many more possibilities with this combination, then one could have if they only had class levels in one of the three.
one could be dexterous fighter, or a wise old man who still has moments when the strength of his youth returns to him, or a contemplative young monk who is questioning his place in the world and wishes to seek out martial arts of distant lands and learn the way of the true warrior.
sometimes though, multi classing can aid a single concept, were the abilities accumulated over many classes and prc give credit to that concept and aid it. Sometimes classes don't need to be all verbs. some can be adverbs that enhance a single class that acts as a verb. Sure this can be done with feats, but its so much more effective to do it with classes. It also adds a degree of respect because again, its better to actually be effective in what you claim your character can do, rather then using up all your feats and still falling short. Its almost like penalizing the tumbling fighter or the sneaky wizard.