The advent of highly segmented gamma-ray detectors with good energy resolution has made a new class of gamma-ray detectors possible. These instruments record the positions and energies of each individual gamma-ray interaction with high precision. Analysis of the individual interactions can provide energy and directional information, even for events with only partial energy deposition. Advantages over traditional gamma-ray detectors include enhanced efficiency, background rejection, gamma-ray imaging, and sensitivity to polarization. Consider those gamma-rays that interact three or more times in the detector. The energy of the gamma-ray that initiated one of these events is uniquely determined by measuring the energies of the first two interactions and the scatter angle of the second interaction. The precision of this measurement is limited by the energy and position resolution of the detector, but also from Doppler broadening that results from gamma-ray scattering off-bound electrons in the detector. It is also essential to correctly sequence the first three interactions. The importance of Doppler broadening is greater in higher Z-materials, thus silicon becomes a good choice for the detector material. We discuss performance and simulations of the multiple Compton telescope. Possible applications include an advanced Compton telescope (ACT) for astrophysics, a medical multiple-gamma detector high-energy imaging survey instrument, and a gamma-ray tracking detector for future low-energy nuclear physics experiments.