Multiple Electrostatic Quadrupole Array Linear Accelerators (MEQALACs) provide an opportunity to realize compact radio-frequency (RF) accelerator structures that can deliver very high beam currents. MEQALACs have been previously realized with acceleration gap distances and beam aperture sizes of the order of centimeters. Through advances in Micro-Electro-Mechanical Systems (MEMS) fabrication, MEQALACs can now be scaled down to the sub-millimeter regime and batch processed on wafer substrates. In this paper, we show first results from using three RF stages in a compact MEMS-based ion accelerator. The results presented show proof-of-concept with accelerator structures formed from printed circuit boards using a 3x3 beamlet arrangement and noble gas ions at 10 keV. We present a simple model to describe the measured results. The model is then used to examine some of the aspects of this approach, such as possible effects of alignment errors. We also discuss some of the scaling behaviour of a compact MEQALAC. The MEMS-based approach enables a low-cost, highly versatile accelerator covering a wide range of beam energies and currents. Applications include ion-beam analysis, mass spectrometry, materials processing, and at very high beam powers, plasma heating.