Sound proof a noisy shower pump in a hot press.

I have a noisy shower pump, and I would like to reduce the level of noise and vibration it makes in the hot press. I have attached pictures of the pump. I have tried to detach the pump from the floor by removing the boards it is sitting on, but I believe the pump may be fixed and/or in place by the connecting pipes. Ideally the noise reduction will be significant from 83.7 db as shown by the attached picture. I would like a solution in which the pump sits on a noise reduction mat or type of rubber that dampens vibrations, and for the whole pump to be encased in a noise-reducing box, possibly made from drywall plasterboard, and perhaps the press being fitted with noise reduction materials. I note that the shower pump may be changed in the next five years. Ideally, if you have experience with shower pumps and noise reduction, that would be great. Thank you and kind regards. Graham Heap Please see the posting on the monobloc bath tap adapter or replacement for a handheld shower attachment. The price is an estimate for work to be completed and excludes material costs.