Although mass spectrometry is well suited to identifying thousands of potential protein post-translational modifications (PTMs), it has historically been biased towards just a few. To measure the entire set of PTMs across diverse proteomes, software must overcome the dual challenges of covering enormous search spaces and distinguishing correct from incorrect spectrum interpretations. Here, we describe TagGraph, a computational tool that overcomes both challenges with an unrestricted string-based search method that is as much as 350-fold faster than existing approaches, and a probabilistic validation model that we optimized for PTM assignments. We applied TagGraph to a published human proteomic dataset of 25 million mass spectra and tripled confident spectrum identifications compared to its original analysis. We identified thousands of modification types on almost 1 million sites in the proteome. We show alternative contexts for highly abundant yet understudied PTMs such as proline hydroxylation, and its unexpected association with cancer mutations. By enabling broad characterization of PTMs, TagGraph informs as to how their functions and regulation intersect.