I recently did a remodel which required a full bathroom. I installed a grinder pump which I believe is different than a grey water pump. The grinder pump will handle solids as well as the grey water. The unit looks like a hard plastic barrel with an output and vent coming out of the top. I simply tied this into an existing 2″ drain already in my basement. You will need to have a way to vent the pump to the outside but this shouldn’t be a problem as you can tie it in with your regular plumbing vent system. I believe cost is around $350 for the entire unit.