In neuroscience, stimulus-response relationships have traditionally been analyzed using either encoding or decoding models. Here we propose a hybrid approach that decomposes neural activity into multiple components, each representing a portion of the stimulus. The technique is implemented via canonical correlation analysis (CCA) by temporally filtering the stimulus (encoding) and spatially filtering the neural responses (decoding) such that the resulting components are maximally correlated. In contrast to existing methods, this approach recovers multiple correlated stimulus-response pairs, and thus affords a richer, multidimensional analysis of neural representations. We first validated the technique's ability to recover multiple stimulus-driven components using electroencephalographic (EEG) data simulated with a finite element model of the head. We then applied the technique to real EEG responses to auditory and audiovisual narratives experienced identically across subjects, as well as uniquely experienced video game play. During narratives, both auditory and visual stimulus-response correlations (SRC) were modulated by attention and tracked inter-subject correlations. During video game play, SRC varied with game difficulty and the presence of a dual task. Interestingly, the strongest component extracted for visual and auditory features of film clips had nearly identical spatial distributions, suggesting that the predominant encephalographic response to naturalistic stimuli is supramodal. The diversity of these findings demonstrates the utility of measuring multidimensional SRC via hybrid encoding-decoding.