I like Push a lot, but I would want to make traits a bit more mechanically relevant. Rolling when a trait applies should make the chances of success higher -- that way, characters also grow in their power when they acquire more (or more powerful) traits. It's been 30 years since I studied probabilities with any complexity, so please verify my math as I go along.
In a normal Push game, the chance of a great success is 2/6 with a single die roll. If you choose to roll another die to add to it, then the chance of getting what you need is, again 2/6. If your original roll was a 4, then you get your great success on a 1 or 2, if you rolled 3 then you need a 2 or 3, etc.
So when using up to two dice, the change of a great success is 2/6 + (4/6 * 2/6), which is just under 56%.
My proposed modification is to allow the player to change the outcome of the second die by one step up or down when the character possesses a trait that would help in that situation. The reasoning is that you are really applying yourself to the task (you're pushing yourself) and your experience/background helps.
Of course, the chance of a great success on the first roll stays 2/6. But on the second roll, your range is much higher. If you rolled a 4 first, you now can get away with a 1, 2 or 3. If you rolled a 3 first, you now can get away with a 1, 2, 3, or 4! If you rolled a 2 first, your range is 2, 3, 4, 5. If you rolled a 1 first, your range is 3, 4, 5 and 6.
The math then comes down to 2/6 + (1/6 * 3/6) + (3/6 * 4/6), which is exactly 75%. Is that a big increase? Probably not, but big enough to make an impact, I think.
If you allow a 'starred' trait to change the result of the second die by up to two steps, then the chance of a great success after the second die comes to a whopping 91%!
What do you think?