Tradeoffs between life history traits impact diverse biological phenomena, including the maintenance of biodiversity. We sought to study two canonical tradeoffs in a model host-parasite system consisting of bacteriophage lambda and Escherichia coli: i) parasite resistance for growth and ii) phage infectivity for host-range. We report that these previously hypothesised tradeoffs are, in fact, tradeups. While the observation of tradeups was surprising, they should be expected because if traits X and Y tradeoff, so too traits Y and Z, then X and Z will tradeup. By considering five different E. coli trait correlations we uncovered several tradeups and tradeoffs. Using mathematical models, we establish that tradeups need not inhibit biodiversity, as previously thought, and can help maintain it through high-dimensional trait interactions. We provide a mechanistic explanation for how tradeups emerge and give reasons for why tradeups can even evolve in well-adapted genomes.