Analysis of large data sets can help resolve difficult nodes in the tree of life and also reveal complex evolutionary histories. The placement of the Celastrales-Oxalidales-Malpighiales (COM) clade within Rosidae remains one of the most confounding phylogenetic questions in angiosperms, with previous analyses placing it with either Fabidae or Malvidae. To elucidate the position of COM, we assembled multi-gene matrices of chloroplast, mitochondrial, and nuclear sequences, as well as large single- and multi-copy nuclear gene data sets. Analyses of multi-gene data sets demonstrate conflict between the chloroplast and both nuclear and mitochondrial data sets, and the results are robust to various character-coding and data-exclusion treatments. Analyses of single- and multi-copy nuclear loci indicate that most loci support the placement of COM with Malvidae, fewer loci support COM with Fabidae, and almost no loci support COM outside a clade of Fabidae and Malvidae. Although incomplete lineage sorting and ancient introgressive hybridization remain as plausible explanations for the conflict among loci, more complete sampling is necessary to evaluate these hypotheses fully. Our results emphasize the importance of genomic data sets for revealing deep incongruence and complex patterns of evolution.