Is it possible to shuffle a 3x3 Rubik's cube so that there's no more than 2 pieces of the same color in every face?

You mean like this?

http://ruwix.com/online-rubiks-cube-solver-program/solution.php?cube=0343515641165422615412533412316442361454656232126363525&x=1

To find the solution just click "play".

EDIT: By the way, the movements to get this setup are:

L R' F' B M' E' U B B

Anyway the question is quite interesting because I think there are not tons of solutions to this problem... so now I have two new questions...

Does anyone knows a shorter way?

How many different combinations of this setup exists?

Protip: In ruwix.com to get the M' and the E' you have to extend the panel by clicking on ">" button

Edit2: This is the shortest algorithm I can imagine...

M' S E M' R U U

The last two steps can be done with U U, D D, F F or B B...

I believe this works. Rotate diagonally opposite pairs of corners so that the front faces move to the sides. Rotate the vertical center slice by a half-turn. Interchange the four edge cubies around the equator.