I'm no expert, but I would think more information is needed to answer your question. Was the pump designed for sewage? Any chance you have the manufacturer and model # so you can check if it is? Is the basement stubbed already?
I have a home I just bought and when it rains, water comes in........... not in a leaking sense but under the wall of the basement in one place I guess there seems to be a crack in the bottom of the wall letting rain water in. What causes this? How do I fix this problem from reoccuring? It's a home built in 1959 and the basement is block foundation and painted.