The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has produced five variants of concern (VOC) to date. The important Spike mutation N501Y is common to Alpha, Beta, Gamma and Omicron VOC, while the P681R is key to the spread of Delta. We have analysed circa 4.2 million SARS-CoV-2 genome sequences from the largest repository Global Initiative on Sharing All Influenza Data (GISAID) and demonstrated that these two mutations have cooccurred on the Spike D614G mutation background at least 3,678 times from 17 October 2020 to 1 November 2021. In contrast, the Y501-H681 combination, which is common to Alpha and Omicron VOC, is present in circa 1.1 million entries. Two-thirds of the 3,678 cooccurrences were in France, Turkey or US (East Coast), and the rest across 57 other countries. 55.5% and 4.6% of the cooccurrences were Alpha Q.4 and Gamma P.1.8 sub-lineages acquiring the P681R; 10.7% and 3.8% were Delta B.1.617.2 lineage and AY.33 sub-lineage acquiring the N501Y; the remaining 10.2% were in other variants. Despite the selective advantages individually conferred by N501Y and P681R, the Y501-R681 combination counterintuitively did not outcompete other variants in every instance we have examined. While this is a relief to worldwide public health efforts, in vitro and in vivo studies are urgently required in the absence of a strong in silico explanation for this phenomenon. This study demonstrates a pipeline to analyse combinations of key mutations from public domain information in a systematic manner and provide early warnings of spread.