In this paper, we first briefly review aspects of inversive geometry and inversive fractals. Motivated by a desire to expand our geometric and artistic toolkit, we then introduce mixed-restriction limit sets as a new technique for use with iterated function systems and groups of circle inversions to create previously undiscovered 2D inversive fractals. We also apply this technique to diverse shape-based inversions that are closely related to circle inversion. Finally, we explore extending mixed-restriction limit sets and shape-based inversions into 3D to generate 3D inversive fractals.