soundproofing sump pump closet
Maybe replacing the pump with a less noisy one would 'help'. You say its submersible,,,is it one where the 'motor' part is also submersed?? Or just the suction foot,pump part?? Those that have motor under water is by nature MUCH more quiet.
Also you MAY want a alarm in CASE it fails and so water doesnt ruin things before you notice. Sometimes the NOISE is sweet music cause it means its working and something ISNT fllooding!!Also you can hear if it is stuck ON!!
Other reason is possible vibration causeing MORE noise than required,,is it vibration of the whole setup or normal run vibration?? try cushioning it and SEE if it quiets down. SOME brands and kinds are MORE noisy than others!!
IF possible you might try wrapping it with something soft, like an old blanket etc. that would muffle sound or build an insulated 'again' box over it to trap MORE sound inside before it gets to the closet walls. Styrofoam is better material for this as it is water tolerate,moisture wise, and deadens alot of sound. Take the excess thick as possible pieces and attach to ceiling yet!! Sound proofing a 'small' closet cant be TOO expensive!!