Perceptual speech quality is an important performance metric for teleconferencing applications. The mean opinion score (MOS) is standardized for the perceptual evaluation of speech quality and is obtained by asking listeners to rate the quality of a speech sample. Recently, there has been increasing research interest in developing models for estimating MOS blindly. Here we propose a multi-task framework to include additional labels and data in training to improve the performance of a blind MOS estimation model. Experimental results indicate that the proposed model can be trained to jointly estimate MOS, reverberation time (T60), and clarity (C50) by combining two disjoint data sets in training, one containing only MOS labels and the other containing only T60 and C50 labels. Furthermore, we use a semi-supervised framework to combine two MOS data sets in training, one containing only MOS labels (per ITU-T Recommendation P.808), and the other containing separate scores for speech signal, background noise, and overall quality (per ITU-T Recommendation P.835). Finally, we present preliminary results for addressing individual rater bias in the MOS labels.