I'm trying to find a mechanic for this concept.  It's a pretty simple concept, and I suck at coming up with mechanics.

Characters start at a competency level of the average human (say grocery store clerk) and *very quickly* advance in power to high-action, matrix-y/wuxia ability.  They do so one bit at a time, gaining new "abilities" as often as once per game session.

The entire focus of the story would necessarily be "Gaining cool powers and dealing with the consequences".

I've looked at "lite" mechanics, like FATE which is too grainy (I think from its FUDGE underpinnings), and HERO and GURPS in which advancement is too un-directed and way too complex.  (That is, advancement is too complex)  Other problems I run into are of a general nature... an example.

Let's say in the area of raw strength.  The Safeway checkout girl -> high-school jock -> police officer -> US Marine -> Punisher -> Blade -> Terminator ->  more steps -> Superman

The game should be playable all along this axis, and advancement should be smooth, simple and highly directed.  And the differences between the grocery clerk and the high-school jock should be noticeable in game.  There should be no doubt when an arm-wrestling bout were to break out that the jock would win.  (it could happen)

One thing I don't want is the Shadowrun solution of shoe-box-full-o-dice....  the mechanics should be fairly simple.  I enjoyed Godlike (well, actually I enjoyed Nemesis), but I can't see it quite stretching to this, or at least my brain isn't getting there with it.  I don't enjoy diceless at all.  It is unsatisfying for me personally.

I'm looking for suggestions, or possibly even pointers towards the kinds of mechanics I'm looking for in the sense of a description.

Hi!
  Have you checked out Shadows of Yesterday? It CAN be pretty similar to this in concept and is a great system. I think the way advancement works in SOY, is probably 80% what you want, maybe more.
  I think Exalted could be used to fast track that kind of advancement, EXCEPT, I don't think it models, normal people too well though...
  Sounds like fun though, lemme know how it goes.

Some Places to Look:
Cartoon Action Hour has a great system for scaling. Also, the old West End Master Book system was good where all the character's stats tied back to those universal benchmark tables. The latest Marvel RPG (Marvel Universe) would also work pretty well as a base, though you have to find a way to add more diversity at lower levels.

Thanks for the pointers.  I had not seen Shadow of Yesterday before, I may have to get that and check it out.  Sounds good on the surface....  and it's cheap, so ...