With great biological interest in post-translational modifications (PTMs), various approaches have been introduced to identify PTMs using MS/MS. Recent developments for PTM identification have focused on an unrestrictive approach that searches MS/MS spectra for all known and possibly even unknown types of PTMs at once. However, the resulting expanded search space requires much longer search time and also increases the number of false positives (incorrect identifications) and false negatives (missed true identifications), thus creating a bottleneck in high throughput analysis. Here we introduce MODa, a novel “multi-blind” spectral alignment algorithm that allows for fast unrestrictive PTM searches with no limitation on the number of modifications per peptide while featuring over an order of magnitude speedup in relation to existing approaches. We demonstrate the sensitivity of MODa on human shotgun proteomics data where it reveals multiple mutations, a wide range of modifications (including glycosylation), and evidence for several putative novel modifications. Based on the reported findings, we argue that the efficiency and sensitivity of MODa make it the first unrestrictive search tool with the potential to fully replace conventional restrictive identification of proteomics mass spectrometry data.