We provide numerical evidence supporting a Bonderson–Slingerland (BS) non-Abelian hierarchy state as a candidate for the observed ν = 12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible ν = 12/5 quantum Hall state with shift S = 2 matching that of the BS state. The exact ground-state of the Coulomb interaction state on the sphere is shown to have large overlap with the BS ground-state trial wavefunction. The analysis of the BS states is extended to hierarchical descendants of general paired states in the weak-pairing phase at ν = 5/2