The reason that many houses do not have a toilet in the basement is due to the lack of space underneath the basement floor. Toilets require space underneath to allow the drain to slope downward to the sewer drain. Most basements have a cement or concrete floor which means that you will have to dig up the floor to add the piping. If there is a lot of head space in the basement — and there usually isn't — you could install the toilet on an elevated surface. This way the toilet will have the space underneath required, and there will not be a need to dig up the concrete floor. A third option is to install a product called a low-bore toilet. It operates like a normal toilet, but with one difference: attached to the toilet is a garbage disposal-type of unit that pumps the liquefied waste up high enough to easily flow down to the main plumbing stack.