Quality prediction for asymmetric multiply-distorted stereoscopic images (MDSIs) confronts more challenges than previous stereoscopic image quality assessment (SIQA) issues, whereas the existing no-reference SIQA methods have been limited to understand the asymmetric distortions and multiple distortions simultaneously for general-purpose blind quality prediction. In this paper, we propose a multistage pooling (MUSP) model for quality prediction of asymmetric MDSIs. In the training stage, we establish multimodal sparse representation framework for phase and amplitude components, respectively. In the testing stage, we use an MUSP strategy to simulate the pooling procedure undergoing multimodal quality pooling, feature pooling, binocular pooling, and phase-amplitude quality pooling in order. Experimental results on our new established database (NBU-MDSID Phase-II) demonstrate the effectiveness of our blind metric.