We consider the magnetically tunable Feshbach resonances that may exist in ultracold mixtures of molecules
in 2 states and alkali-metal atoms. We focus on Rb+CaF as a prototype system. There are likely to be Feshbach
resonances analogous to those between pairs of alkali-metal atoms. We investigate the patterns of near-threshold
states and the resonances that they cause, using coupled-channel calculations of the bound states and low-energy
scattering on model interaction potentials. We explore the dependence of the properties on as-yet-unknown
potential parameters. There is a high probability that resonances will exist at magnetic fields below 1000 G,
and that these will be broad enough to control collisions and form triatomic molecules by magnetoassociation.
We consider the effects of CaF rotation and anisotropy of the interaction potential, and conclude that they may
produce additional resonances but should not affect the existence of rotation-free resonances.