The refinement you're talking about here isn't so much a matter of modifying an incorrect but exact definition as it is clarifying an irrefutable but ambiguous definition.

That said, maybe something could come of this if you truly got to the very basic building blocks. For instance, an integer is just a definition - an exact one, but a definition nonetheless. So we can define a rational number as the ratio of two integers, and then build a refutable hypothesis from it - that all numbers are either integers or the ratio of integers.

I have serious doubts as to whether "self interest" could ever be defined as precisely as an integer, though.

"Ratio", "Square Root", and "Integer" have precise definitions, whereas "self interest" is imprecise.

Try this out: at a dinner party (one that you don't care if you're invited back), declare that "all people act out of self-interest, ultimately."

Odds are good that two people will disagree quite vehemently about this, and at the core will be a fundamental disagreement about what it means to be "self-interested".