Sometimes getting the plumbing groundwork into a shallow space can be challenging, but it is usually possible to install a full bathroom in most basements. Occasionally a sewage ejector (sump pump) requried, for instance if your sewer pipe exits the basement wall instead of the ground, this is quite rare.
The following pictures are a few of my many basement projects.
Where depth is an issue, A floor mounted - rear outlet toilet can make possible a bathroom where it couldn't work otherwise. These toilets are also useful in attic bathrooms where it is not possible to drill shallow floor joists. Top picture shows the new "rough-in" for the rear-outlet toilet.
New clothes washer location. Some customers opt to keep their basement location and install and additional clothes washer location on the second floor level to avoid carrying laundry down to the basement. Stackable washer and dryer units are always an option in tight spaces.