Whole genome duplication (WGD) brings challenges to key processes like meiosis, but nevertheless is associated with diversification in all kingdoms. How is WGD tolerated, and what processes commonly evolve to stabilize the new polyploid lineage? Here we study this inCochleariaspp., which have experienced multiple rounds of WGD in the last 300,000 years. We first generate a chromosome-scale genome and sequence 113 individuals from 33 diploid, tetraploid, hexaploid, and outgroup populations. We detect the clearest post-WGD selection signatures in functionally interacting kinetochore components and ion transporters. We structurally model these derived selected alleles, associating them with known WGD-relevant functional variation and compare these results to independent recent post-WGD selection inArabidopsis arenosaandCardamine amara. Some of the same biological processes evolve in all three WGDs, but specific genes recruited are flexible. This points to a polygenic basis for modifying systems that control the kinetochore, meiotic crossover number, DNA repair, ion homeostasis, and cell cycle. Given that DNA management (especially repair) is the most salient category with the strongest selection signal, we speculate that the generation rate of structural genomic variants may be altered by WGD in young polyploids, contributing to their occasionally spectacular adaptability observed across kingdoms.