They can, that's what we call cancer... it's some of our cells rebelling and deciding to do their own thing, and to hell with the superorganism. Of course that isn't all that smart since the cancer will die when we die, right? Well, maybe not... although I don't know of any documented case in humans, some cancers are known to migrate off their original organism and colonize others! An example of this is the tasmanian devil face cancer... it started on one individual and spread to others, the tumors on all infected devils having the genes of the original individual.
But what about individual cells? Surely the buck stops there and they are individual, indivisible organisms? Not so fast! Cells of all eucaryotes (that's us) contain "organs" (mitochondria) that were once a separate form of life and still have their own genetic code, completely separate from the nuclear genetic code of our cells. Not only that, but it was recently discovered that they are still independent enough that they can migrate from one cell to another on their own.
So, yeah, "individual organism" is an abstract concept that has different meanings at different scales and even at a specific scale is rather fluid. And I think "individual self" (or mind) is like that too, but that's another story...