Starting with generic Wess-Zumino type coupling to constant four-form and the dual seven-form field strengths in the ABJM theory, we obtain mass-deformed theories with N = 2, 4 supersymmetries. These theories contain massless scalar fields and allow the implementation of the Mukhi-Papageorgakis Higgsing procedure. Using this procedure, we connect the Higgsed theories to three-dimensional mass-deformed SYM theories. These are also connected by the four-dimensional N = 1 * , 2 * mass-deformed SYM theories through dimensional reduction. We classify the three-dimensional mass-deformed SYM theories of N = 1, 2, 4 supersymmetry, of which a few cases of N = 1, 2 are connected neither by MP Higgsing procedure nor dimensional reduction.