Whole genome duplication (WGD) occurs across kingdoms and can promote adaptation. However, the sudden increase in chromosome number, as well as immediate changes in cellular physiology, are traumatic to conserved cellular processes. Previous work in Arabidopsis arenosa revealed a clearly coordinated genomic response to WGD, involving a set of functionally and physically interacting proteins mediating crossover number and distribution during prophase I of meiosis. Here we ask: is this highly coordinated coevolutionary shift repeated in other species? We also test globally for convergence for all processes under selection in independent cases of adaptation to WGD, as other processes were under selection in A. arenosa and may be common to other independent adaptation events following WGD. Taking advantage of a well-characterised diploid/autopolyploid system, Cardamine amara, we test our hypothesis that convergence will be detected in the form of directional selection. We also investigate at what level convergence may be evident: identical genes, networks, or analogous processes. To do this we performed a genome scan between diploid and autotetraploid populations, while utilising a quartet-based sampling design to minimise false positives. Among the genes exhibiting the strongest signatures of selection in C. amara autotetraploids we detect an enrichment for DNA maintenance, chromosome organisation, and meiosis, as well as stress signalling. We find that gene-level convergence between the independent WGD adaptation events in C. amara and A. arenosa is negligible, with no more orthologous genes in common than would be expected by chance. In contrast to this, however, we observe very strong convergence at the level of functional processes and homologous (but not orthologous) genes. Taken together, our results indicate that these two autopolyploids survived the challenges attendant to WGD by modifying similar or identical processes through different molecular players and gives the first insight into the salient adaptations required to cope with a genome-doubled state.