Context. Complex organic molecules are detected in many sources in the warm inner regions of envelopes surrounding deeply embedded protostars. Exactly how these species form remains an open question. Aims. This study aims to constrain the formation of complex organic molecules through comparisons of their abundances towards the Class 0 protostellar binary IRAS 16293–2422. Methods. We utilised observations from the ALMA Protostellar Interferometric Line Survey of IRAS 16293–2422. The species identification and the rotational temperature and column density estimation were derived by fitting the extracted spectra towards IRAS 16293–2422 A and IRAS 16293–2422 B with synthetic spectra. The majority of the work in this paper pertains to the analysis of IRAS 16293–2422 A for a comparison with the results from the other binary component, which have already been published. Results. We detect 15 different complex species, as well as 16 isotopologues towards the most luminous companion protostar IRAS 16293–2422 A. Tentative detections of an additional 11 isotopologues are reported. We also searched for and report on the first detections of methoxymethanol (CH₃OCH₂OH) and trans-ethyl methyl ether (t-C₂H₅OCH₃) towards IRAS 16293–2422 B and the follow-up detection of deuterated isotopologues of acetaldehyde (CH₂DCHO and CH₃CDO). Twenty-four lines of doubly-deuterated methanol (CHD₂OH) are also identified. Conclusions. The comparison between the two protostars of the binary system shows significant differences in abundance for some of the species, which are partially correlated to their spatial distribution. The spatial distribution is consistent with the sublimation temperature of the species; those with higher expected sublimation temperatures are located in the most compact region of the hot corino towards IRAS 16293–2422 A. This spatial differentiation is not resolved in IRAS 16293–2422 B and will require observations at a higher angular resolution. In parallel, the list of identified CHD₂OH lines shows the need of accurate spectroscopic data including their line strength.