Our aim is to develop quantitative single-molecule assays to study when and where molecules are interacting inside living cells and where enzymes are active. To this end we present a three-camera imaging microscope for fast tracking of multiple interacting molecules simultaneously, with high spatiotemporal resolution. The system was designed around an ASI RAMM frame using three separate tube lenses and custom multi-band dichroics to allow for enhanced detection efficiency. The frame times of the three Andor iXon Ultra EMCCD cameras are hardware synchronized to the laser excitation pulses of the three excitation lasers, such that the fluorophores are effectively immobilized during frame acquisitions and do not yield detections that are motion-blurred. Stroboscopic illumination allows robust detection from even rapidly moving molecules while minimizing bleaching, and since snapshots can be spaced out with varying time intervals, stroboscopic illumination enables a direct comparison to be made between fast and slow molecules under identical light dosage. We have developed algorithms that accurately track and co-localize multiple interacting biomolecules. The three-color microscope combined with our co-movement algorithms have made it possible for instance to simultaneously image and track how the chromosome environment affects diffusion kinetics or determine how mRNAs diffuse during translation. Such multiplexed single-molecule measurements at a high spatiotemporal resolution inside living cells will provide a major tool for testing models relating molecular architecture and biological dynamics.