  We consider the long-range states expected for complexes formed from an
alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We
explore the structure of the Hamiltonian for such systems, and the couplings
between the six angular momenta that are present. We consider the patterns and
densities of the long-range states, and the terms in the Hamiltonian that can
cause Feshbach resonances when the states cross threshold as a function of
magnetic field. We present a case study of $^{40}$K$^{87}$Rb+$^{87}$Rb. We show
multiple types of resonance due to long-range states with rotational and/or
hyperfine excitation, and consider the likelihood of them existing at low to
moderate magnetic fields.
