Expanding and reprogramming the genetic code of cells for the incorporation of multiple distinct non-canonical amino acids (ncAAs), and the encoded biosynthesis of non-canonical biopolymers, requires the discovery of multiple orthogonal aminoacyl-transfer RNA synthetase/tRNA pairs. These pairs must be orthogonal to both the host synthetases and tRNAs and to each other. Pyrrolysyl-tRNA synthetase (PylRS)/PyltRNA pairs are the most widely used system for genetic code expansion. Here, we reveal that the sequences of ΔNPylRS/ΔNPyltRNA pairs (which lack N-terminal domains) form two distinct classes. We show that the measured specificities of the ΔNPylRSs and ΔNPyltRNAs correlate with sequence-based clustering, and most ΔNPylRSs preferentially function with ΔNPyltRNAs from their class. We then identify 18 mutually orthogonal pairs from the 88 ΔNPylRS/ΔNPyltRNA combinations tested. Moreover, we generate a set of 12 triply orthogonal pairs, each composed of three new PylRS/PyltRNA pairs. Finally, we diverge the ncAA specificity and decoding properties of each pair, within a triply orthogonal set, and direct the incorporation of three distinct non-canonical amino acids into a single polypeptide.