The discovery of Chromera velia, a free-living photosynthetic relative of apicomplexan pathogens, has provided an unexpected opportunity to study the algal ancestry of malaria parasites. In this work, we compared the molecular footprints of a eukaryote-to-eukaryote endosymbiosis in C. velia to their equivalents in peridinin-containing dinoflagellates (PCD) to reevaluate recent claims in favor of a common ancestry of their plastids. To this end, we established the draft genome and a set of full-length cDNA sequences from C. velia via next-generation sequencing. We documented the presence of a single coxI gene in the mitochondrial genome, which thus represents the genetically most reduced aerobic organelle identified so far, but focused our analyses on five “lucky genes” of the Calvin cycle. These were selected because of their known support for a common origin of complex plastids from cryptophytes, alveolates (represented by PCDs), stramenopiles, and haptophytes (CASH) via a single secondary endosymbiosis with a red alga. As expected, our broadly sampled phylogenies of the nuclear-encoded Calvin cycle markers support a rhodophycean origin for the complex plastid of Chromera. However, they also suggest an independent origin of apicomplexan and dinophycean (PCD) plastids via two eukaryote-to-eukaryote endosymbioses. Although at odds with the current view of a common photosynthetic ancestry for alveolates, this conclusion is nonetheless in line with the deviant plastome architecture in dinoflagellates and the morphological paradox of four versus three plastid membranes in the respective lineages. Further support for independent endosymbioses is provided by analysis of five additional markers, four of them involved in the plastid protein import machinery. Finally, we introduce the “rhodoplex hypothesis” as a convenient way to designate evolutionary scenarios where CASH plastids are ultimately the product of a single secondary endosymbiosis with a red alga but were subsequently horizontally spread via higher-order eukaryote-to-eukaryote endosymbioses.