Okay, so having five stats is okay for Apocalypse World, because it's a rather constrained setting, but my normal inclination would be to have more stats. Probably seven, by separating technical aptitude and psychic powers, and maybe separating cool into covert and overt, so there's a stealth stat. Or whatever else would fit a new setting—there's plenty of settings where magic, psionics, luck, knowledge, and the ability to make machines should all be separate stats instead of weird. And also, with five it's pretty easy to max out all your stats. Actually, it's pretty easy given the –2 to +3 range, but whatever.
Still, I like the four stats. And then I thought about a different style of dice mechanic. What if your stats are rated 1-4, so you give each one a different number. That's how many dice you roll, and you keep the two highest. So, if your stats is 2, roll 2d6. If your stat is 4, roll 4d6 and count the two highest ones.
If your stat is 1, either you roll 1d6 (which kinda sucks—I'll get to bonuses later), or you rate it P instead of 1, and roll 3d6 and keep the two lowest. So you still get a range of 2-12, just like the other stats, but it's considerably worse. Anyway, that gives a much different curve than straight +1 or +2 does (I think, anyway).
So, how do you get bonuses to your roll? Here is where having more than five stats comes in. You have additional tags for your stats that give you bonuses in certain situations, and you can use gear and other special bonuses.
And that's how I came up with this:
Assign amongst Cool, Heavy, Social, and Deep the following four scores: 2, 3, 4, and P.
When you avoid interference, roll your cool.
...and when you evade pursuit or detection, roll cool+evade.
...and when you resist pressure, roll cool+resist.
When you show your strength, roll your heavy.
...and when you commit assault, roll heavy+assault.
...and when you recover from shock, harm, or setbacks, roll heavy+recover.
When you manipulate someone, roll your social.
...and when you dissect someone, roll social+dissect.
...and when you make a deal, roll social+deal.
And then Deep gets a bit more complicated. Basically, it's the same as Echoes, you roll it to establish a node, and then you get a sync score in that node, and when you tap the node, your roll+sync.
When you look into something, there are three acknowledged levels. Level 1 is reality, the physical world. When you look deep into the real world, roll deep+sense (or deep+investigate or search maybe?). Level 0 is under-reality, the flat world of data, information in books and bytes, out there on the interwebs somewhere. When you dredge through Level 0, looking into it (whatever "it" is), roll deep+research. Level 2 is inside your mind. It's not connected to anybody else's mind, so you can only go deep into your own mind. When you do, roll deep+recall.
Psychic powers also occur on Level 2, and sometimes on Level 1...
You can get skills that act as bonuses, from your playbook or whatever:
Combat training, +1assault.
Iron will, +1resist.
Sex appeal, +1dissect.
Silver tongue, +1deal.
Eidetic memory, +1recall.
Or, you can get skills that act like permanent nodes, for example:
Rocket science (sync+2)
Ancient history (sync=0)
That's what your stat thread made me do, Nathan.