Crystalline gold nanoprisms of sub-micrometric size sustain high order plasmon modes in the visible and near infrared range that open a new realm for plasmon modal design, integrated coplanar devices and logic gates. In this article, we explore the tailoring of the surface plasmon local density of states (SP-LDOS) by embedding a single defect, namely a small hole, carved in the platelet by focused ion beam (FIB). The change in the SP-LDOS of the hybrid structure is monitored by two-photon luminescence (TPL) microscopy. The dependency of the two-dimensional optical field intensity maps on the linear polarization of the tightly focused femtosecond laser beam reveals the conditions for which the hole defect significantly affects the initial modes. A detailed numerical analysis of the spectral characteristics of the SP-LDOS based on the Green dyadic method clearly indicates that the hole size and location can be exploited to tune or remove selected SP modes.