Yes, it is not only possible to add a basement drainage system after the house is finished, it is done with great frequency. Many homes are built today with some kind of drainage system to protect and seal the basement against water leaks or seepage.

There are several ways to seal a basement, some better than others. Some drainage systems are installed and provide protection from outside the walls and beneath the floor of the basement. These can be expensive to install because of the amount of work involved. Other systems are installed on the inside of the basement and work to channel moisture down to a drain at the juncture of the wall and the floor (which is where many leaks occur). These might drain to the exterior of the home, perhaps down a hill, or they empty into a drain that contains a sump pump to draw the moisture.

Either approach should be installed only by a professional. This is not a job for a do-it-yourselfer.