In this paper, we have theoretically explored the third-order and fifth-order nonlinear susceptibilities for a semiconductor quantum dot in a hybrid system composed of a semiconductor quantum dot, metal nanoparticle, and graphene nanodisk. We considered the dipole-dipole interaction induced by the applied field assuming continuous-wave electromagnetic field enhancement in the quantum dot. The semiconductor quantum dot in the MNP-SQD-GND hybrid system exhibits analytically obtained third- and fifth-order susceptibilities, which are described by means of the density matrix approach. As a function of the applied field frequency detuning, we were able to obtain the spectra of the third- and fifth-order susceptibilities for a variety of parameters, including the metal nanoparticle radius, material, orientation, and arrangement within the hybrid system, as well as the interparticle angles and distances. Additionally, we looked into the effects of having the graphene nanodisk present or absent. The outcomes showed that there was a considerable variation in the semiconductor quantum dot's nonlinear optical response when each of these factors was changed. In particular, the presence of the graphene nanodisk led to a substantial enhancement in the nonlinear optical response of the quantum dot in this hybrid system influenced by the dipole-dipole interaction. The results suggest an increased nonlinearity of the semiconductor quantum dot within this hybrid system.