Our contribution focuses at improving the image reconstruction process for specific Compton imaging systems able to detect multiple classes of events, in the field of nuclear imaging. For each existing prototype of such systems, one or several processing methods have already been proposed to retrieve the activity map. Most of them get their inspiration from maximum likelihood expectationmaximization (MLEM), but none of them actually compute the MLEM solution. Some exploit the fully detected events only (e.g. in threegamma imaging, the simultaneous detection of a pair of annihilation photons and of a third photon), and other combine several classes of detected events in a suboptimal way. In this paper, we first introduce a general framework for the reconstruction of a single activity map from multi-class events, and we provide the suited list-mode MLEM update equation. We then consider the case of XEMIS2, a preclinical prototype of a Compton telescope for three-gamma imaging, for which four distinct classes of partial detections coexist with the full detection class. As a preliminary step towards effective multi-class reconstruction, we generate a sensitivity map for the five classes using a dedicated Monte Carlo simulator.