Parametrically-resonant micro-mirrors have proven highly effective in generating large amplitude, high-frequency motion for laser scanning in endoscopic microscopy, using Lissajous scan patterns to create a 2D image. However, Lissajous scanning produce low scanning density at the center of an image. In this work, a strategy for exciting additional harmonic behavior in a parametrically-resonant electrostatic micro-mirror is identified. The mirror’s nonlinear dynamics produce substantial changes in natural frequency with bias voltage. This allows a biased, duty-cycled square wave to produce higher harmonic oscillations that can be naturally synchronized with primary resonance in integer ratios. This in turn allows for alternate scanning distributions in 2D imaging that increase pixel sampling near the center of an image. In simulation, use of a biased square wave signal is found to be capable of producing steady-state oscillations at first and third harmonics of natural frequency for a micro-mirror operated via parametric resonance. Multiple harmonic motion is also realized without increasing input voltage amplitude beyond nominal amplitude, with a greater than 50% reduction fill time for the center of the imaging region. Parameterized relationships between input and output oscillations are identified, sensitivity of output trajectory to model variation, and impact on scanning density for a 2D MEMS micro-mirror are briefly described.