This paper introduces a nonlinear vector-based feature mapping approach to extract robust features for automatic speech recognition (ASR) of overlapping speech using a microphone array. We explore different configurations and additional sources of information to improve the effectiveness of the feature mapping. First, we investigate the full-vector based mapping of different sources in a log mel-filterbank energy (log MFBE) domain, and demonstrate that retraining the acoustic model using the generated training data can help improve the recognition performance. Then we investigate the feature mapping between different domains. Finally in order to improve the qualities of the mapping inputs we propose a nonlinear mapping of the features from multiple beamformed sources, which are directed at the target and interfering speakers, respectively. We demonstrate the effectiveness of the proposed approach through extensive evaluations on the MONC corpus, which includes non-overlapping single speaker and overlapping multi-speaker conditions.