The unbounded permutations of biological molecules, including proteins and their constituent peptides, present a dilemma in identifying the components of complex biosamples. Sequence search algorithms used to identify peptide spectra can be expanded to cover larger classes of molecules, including more modifications, isoforms, and atypical cleavage, but at the cost of false positives or false negatives due to the simplified spectra they compute from sequence records. Spectral library searching can help solve this issue by precisely matching experimental spectra to library spectra with excellent sensitivity and specificity. However, compiling spectral libraries that span entire proteomes is pragmatically difficult. Neural networks that predict complete spectra containing a full range of annotated and unannotated ions can be used to replace these simplified spectra with libraries of fully predicted spectra, including modified peptides. Using such a network, we created predicted spectral libraries that were used to rescore matches from a sequence search done over a large search space, including a large number of modifications. Rescoring improved the separation of true and false hits by 82%, yielding an 8% increase in peptide identifications, including a 21% increase in nonspecifically cleaved peptides and a 17% increase in phosphopeptides.