Successfully modeling overlapping speech is a crucial step towards improving the performance of current speaker diarization systems. In this direction, we present ongoing work on a novel Multi-Class Vector Taylor Series (MC-VTS) approach that models overlapping speech from knowledge of the individual speaker models and the feature extraction process. We explore several variants of the MC-VTS technique that aim at modeling overlapping speech more precisely. Bootstrapping the algorithm with both oracle and diarization output segmentations, we show the potential of this approach in terms of overlapping speech detection and speaker labeling performances through a set of experiments on far-field microphone meeting data.