We investigated the effect of nonadsorbing polymer on the phase behavior of suspensions of positively charged Mg2Al layered double hydroxide (LDH) platelets by birefringence observations and rheological measurements. We show that the depletion attraction, induced by the addition of a high-molecular-weight polyvinyl pyrrolidone (PVP), enriches the phase behavior of these electrostatically stabilized suspensions. At intermediate LDH and polymer concentration, two isotropic phases (I-1-I-2) coexist, nematic-nematic (N-1-N-2) demixing occurs, and a sediment phase is observed, with the appearance of two-, three-, four-, and even six-phase coexistence. Upon increasing the polymer concentration, the I-N phase transition and the sol-gel transition shift to lower LDH concentrations; meanwhile, the I-N coexistent samples enter the purely nematic phase. We explain the richness of the phase behavior in such LDH-PVP mixtures by discussing the interactions among PVP-induced depletion attraction, particle polydispersity, and particle sedimentation.