SCC did an article about that a few years ago. They put a series of +1, +2 and +3 packages (with the same model tire) on a Civic or something and tested it.
But really there are too many variables to say that just bolting on wider tires without changing anything else will make your car handle better. Start with the camber change inherent in a strut suspension. There's a reason guys who run monster-meat tires also run suspensions that limit travel with huge spring rates and sway bars.
Also, grip does not always equal perceived good handling. How many times do tires with higher absolute limits feel worse in the real world?
As always, no simple answer unless you limit your question so much that the answer doesn't matter.