This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique for which the authors have constructed a fast direct solver. The key features of the work presented in this paper are that the fast direct solver is more efficient for the new extended linear system and that problems involving specialized quadrature for weakly singular kernels can be easily handled. Numerical results illustrate the improved performance of the fast direct solver for the new extended system when compared to the fast direct solver for the original extended system. •A locally perturbed geometry differs from the original in local portion of the boundary.•Local refinement in boundary discretization is also regarded as local perturbation.•Extended systems allow for linearly scaling direct solvers for the perturbed problem.•The solver built for the original problem is reused to solve the perturbed one.