This research introduces an enhanced version of the multi-objective speech assessment model, called MOSA-Net+, by leveraging the acoustic features from large pre-trained weakly supervised models, namely Whisper, to create embedding features. The first part of this study investigates the correlation between the embedding features of Whisper and two self-supervised learning (SSL) models with subjective quality and intelligibility scores. The second part evaluates the effectiveness of Whisper in deploying a more robust speech assessment model. Third, the possibility of combining representations from Whisper and SSL models while deploying MOSA-Net+ is analyzed. The experimental results reveal that Whisper's embedding features correlate more strongly with subjective quality and intelligibility than other SSL's embedding features, contributing to more accurate prediction performance achieved by MOSA-Net+. Moreover, combining the embedding features from Whisper and SSL models only leads to marginal improvement. As compared to MOSA-Net and other SSL-based speech assessment models, MOSA-Net+ yields notable improvements in estimating subjective quality and intelligibility scores across all evaluation metrics. We further tested MOSA-Net+ on Track 3 of the VoiceMOS Challenge 2023 and obtained the top-ranked performance.