In this paper we consider a well-known construction due to Gromov and Lawson, Schoen Yau, Gajer, Walsh which allows for the extension of metric positive scalar curvature over trace surgery in codimension at least $3$ is product near boundary. We generalize work $(p,n)$-intermediate $0\leq p\leq n-2$ surgeries $p+3$. then use it well known theorem Carr. Letting ${\cal R}^{s_{p,n}>0}(M)$ denote s...