Recent research demonstrates that large language models can predict neural activity recorded via electrocorticography during natural language processing. To predict word-by-word neural activity, most prior work evaluates encoding models within individual electrodes and participants, limiting generalizability. Here we analyze electrocorticography data from eight participants listening to the same 30-min podcast. Using a shared response model, we estimate a common information space across participants. This shared space substantially enhances large language model-based encoding performance and enables denoising of individual brain responses by projecting back into participant-specific electrode spaces-yielding a 37% average improvement in encoding accuracy (from r = 0.188 to r = 0.257). The greatest gains occur in brain areas specialized for language comprehension, particularly the superior temporal gyrus and inferior frontal gyrus. Our findings highlight that estimating a shared space allows us to construct encoding models that better generalize across individuals.