So, I really like having several tiers of mastery in skills. I don’t like huge static modifiers, however.
What if base proficiency gets you the proficiency bonus, but after that you have mastery ranks that get you a larger bonus die? Not a stack of dice, but like d4 through d12 as you gain mastery.
Mm. Kind of Alternity-esque.
In a system that has pass/fail without gradation or levels of success, however, it looks better than it actually is. Sure, having multiple dice makes your average performance more reliable. It also opens up very high target numbers. That looks awesome, but the character won't generally be able to hit those when they really need it, and they get no advantage from them when they happen accidentally.
Depending what you are looking for, you might get more out of, "If you roll under a X, treat the die as X," where X goes up with levels of mastery.