Many cases of rapid evolutionary radiations in plant and animal lineages are known; however phylogenetic relationships among these lineages have been difficult to resolve by systematists. Increasing amounts of genomic data have been sequentially applied in an attempt to resolve these radiations, dissecting their evolutionary patterns into a series of bifurcating events. Here we explore one such rapid radiation in the tropical plant order Zingiberales (the bananas and relatives) which includes eight families, approximately 110 genera, and more than 2,600 species. One clade, the "Ginger families", including (Costaceae Zingiberaceae) (Marantaceae Cannaceae), has been well-resolved and well-supported in all previous studies. However, well-supported reconstructions among the "Banana families" (Musaceae, Heliconiaceae, Lowiaceae, Strelitziaceae), which most likely diverged about 90 Mya, have been difficult to confirm. Supported with anatomical, morphological, single locus, and genome-wide data, nearly every possible phylogenetic placement has been proposed for these families. In an attempt to resolve this complex evolutionary event, hybridization-based target enrichment was used to obtain sequences from up to 378 putatively orthologous low-copy nuclear genes (all ≥ 960 bp). Individual gene trees recovered multiple topologies among the early divergent lineages, with varying levels of support for these relationships. One topology of the "Banana families" (Musaceae (Heliconiaceae (Lowiaceae Strelitziaceae))), which has not been suggested until now, was almost consistently recovered in all multilocus analyses of the nuclear dataset (concatenated - ExaML, coalescent - ASTRAL and ASTRID, supertree - MRL, and Bayesian concordance - BUCKy). Nevertheless, the multiple topologies recovered among these lineages suggest that even large amounts of genomic data might not be able to fully resolve relationships at this phylogenetic depth. This lack of well-supported resolution could suggest methodological problems (i.e., violation of model assumptions in both concatenated and coalescent analyses) or more likely reflect an evolutionary history shaped by an explosive, rapid, and nearly simultaneous polychotomous radiation in this group of plants towards the end of the Cretaceous, perhaps driven by vertebrate pollinator selection.