There may be better answers but cork would absorb midrange. Acoustic tile is essentially fake painted cork but the paint hinders sound absorb. The "Midrange" bracket is very broadband depending on your definition. At it's widest it can be from 600hz to 2500 hz in my definition.
If you can give a frequency range, I'd bet you will obtain more focused answers for your problem. Carpet, especially fuzzy carpet deep-pile absorbs all sorts of waves above bass when hanging on a wall or attached to a ceiling. It also absorbs odors and is hard to clean on vertical walls and on ceilings.
You can get weird on it by using cork, for example, in pieces sticking out from the wall, or carpet in tight loops sticking out from the wall too. Foam absorbs midrange. Another way is to cut foam, for example, into squares or whatever a couple inches thick, wide, and long and attaching them all over the walls, adding more until the sound balance is right for you.
Old school Live End Dead End used the sound absorbant treatment on the dead end wall around and behind the engineer or mixer. Up Down Left Right and Behind. I saw a lot of shag carpeting on the walls, ceilings, and on the floor beginning at the mix desk.
With a cement wall, I'd first glue foam rubber style material at 1/2 to 1" or so then attach to it some some cork or carpet depending on the midrange frequencies needed to be dampened. The cement wall snap-back will be absorbed. Too much is a truly dead room. Just to stop cement wall snap, even a layer of spray foam could do it depending on the sound level.
I'm sure a lot of others have other ideas; these are off the cuff ideas based on observation of ye olde 70's studios. May not be the best.