Recent multi-gene phylogenetic analyses of plastid-encoded genes have recovered a robust monophyly of chlorophyll-c containing plastids (Chl-c palstids) in cryptophytes, haptophytes, photosynthetic stramenopiles, and dinoflagellates. However, all the plastid multi-gene phylogenies published to date utilized the "linked" model, which ignores the heterogeneity of sequence evolution across genes in alignments. Both empirical and simulation studies show that, compared to the linked model, the "unlinked" model, which accounts for gene-specific evolution, can greatly improve multi-gene estimations. Here we newly sequenced 46 genes of Chl-c plastids, and examined the Chl-c plastid evolution by multi-gene analyses under the unlinked model. Unexpectedly, Chl-c plastid monophyly received only low to medium support in our analyses based on multi-gene data sets including up to 4829 alignment positions. Although we systematically surveyed and excluded the genes that could mislead estimation, the (inconclusive) support for Chl-c plastid monophyly was not significantly altered. We conclude that the estimates from the current plastid-encoded gene data are insufficient to resolve Chl-c plastid evolution with confidence, and are highly affected by genes subjected to the analyses, and methods for tree reconstruction applied. Thus, future data analyses of larger multi-gene data sets, preferentially under the unlinked model, are required to conclusively understand Chl-c plastid evolution.