An extended version of the equalization-cancellation (EC) model of binaural processing is described and applied to speech intelligibility tasks in the presence of multiple maskers. The model incorporates time-varying jitters, both in time and amplitude, and implements the equalization and cancellation operations in each frequency band independently. The model is consistent with the original EC model in predicting tone-detection performance for a large set of configurations. When the model is applied to speech, the speech intelligibility index is used to predict speech intelligibility performance in a variety of conditions. Specific conditions addressed include different types of maskers, different numbers of maskers, and different spatial locations of maskers. Model predictions are compared with empirical measurements reported by Hawley et al. [J. Acoust. Soc. Am. 115, 833-843 (2004)] and by Marrone et al. [J. Acoust. Soc. Am. 124, 1146-1158 (2008)]. The model succeeds in predicting speech intelligibility performance when maskers are speech-shaped noise or broadband-modulated speech-shaped noise but fails when the maskers are speech or reversed speech.