The Supporting Hyperplane Optimization Toolkit (SHOT) solver was originally developed for solving convex MINLP problems, for which it has proven to be very efficient. In this paper, we describe some techniques and strategies implemented in SHOT for improving its performance on nonconvex problems. These include utilizing an objective cut to force an update of the best known solution and strategies for handling infeasibilities resulting from supporting hyperplanes and cutting planes generated from nonconvex constraint functions. For convex problems, SHOT gives a guarantee to find the global optimality, but for general nonconvex problems it will only be a heuristic. However, utilizing some automated transformations it is actually possible in some cases to reformulate all nonconvexities into linear form, ensuring that the obtained solution is globally optimal. Finally, SHOT is compared to other MINLP solvers on a few nontrivial test problems to illustrate its performance.