I know that Discover has a card with a 5% discount category that changes once a quarter. Everything not in the category gets 1%. It's not hard to get the card (or at least wasn't) and was frequently advertised to college students.
If you combine that with a card that gives 2% on everything than it wouldn't be hard to average over 2% cashback as long as you were mindful about using the discover card for qualifying purchases and the 2% card for everything else.
There is one other rub - because I use my bank's card I get better interest rates. How does a .25-.5 % on my various loans and checking account compare to 2% on groceries - this is a complex question that it not easy to answer.
If you combine that with a card that gives 2% on everything than it wouldn't be hard to average over 2% cashback as long as you were mindful about using the discover card for qualifying purchases and the 2% card for everything else.