In this thesis we consider a well known construction due to Gromov, Lawson, and Gajer which allows for the extension of a metric of positive scalar curvature over the trace of a surgery in codimension at least 3 to a metric of positive scalar curvature which is a product near the boundary. We generalize this construction to work for (p; n)-intermediate scalar curvature for for surgeries in codimension at least p + 3.