muffle up
To dampen or silence a loud noise. A noun or pronoun can be used between "muffle" and "up." The assassin used a pillow to muffle up the sound of the gun. I put on extra thick socks to muffle my footsteps up, but Tom was still able to hear me. The walls in our apartment do almost nothing to muffle up the sounds coming from the adjoining room.
muffle something up
to deaden or stifle a sound. Betty tried to muffle the sounds up, but everyone heard what was going on. She muffled up the sounds.