Consider Jeffrey Barrett's traveling minds interpretation of Quantum Mechanics (see also here). On this interpretation, minds traverse a branching Everett-style multiverse in accordance with the probabilities given by the Born rule. But unlike on the Albert-Loewer many-minds interpretation, the minds are constrained to travel together: they are always found in the same branch of the universe.
Here is something interesting about the position in logical space of this interpretation. It is a hidden-variables interpretation in the sense that it supposes that there are realities that cannot be reduced to the wavefunction. The hidden variables on this story correspond to facts about brain states. For instance, the wavefunction may place my brain in a superposition of a brain state in which I feel I am sitting with a state in which I feel I am standing, but the minds (jointly) pick out a branch of the wavefunction--the one in which I feel I am sitting (and writing a post on quantum mechanics). Notice, however, that the hidden variables in this story are hidden from the wavefunction but not hidden from us: they are phenomenally accessible to us.
Interestingly, the Bohm interpretation can be seen also to be a hidden-variables interpretation where the variables are not entirely hidden from us. For presumably it is the "hidden" positions of the particles that determine the brain state that gives rise to my phenomenal state. So from my phenomenal state, I can tell something about the hidden variables--for instance, that they comprise a brain. Bohm is a paradigmatic hidden variable interpretation, and yet it does not actually hide the variables from us. So we need to be cautious about the phrase "hidden variables".
I think the Albert-Loewer many-minds interpretation is also a hidden variable theory. The variables are the states of the many minds. But there is a difference between the Barrett and Albert-Lower interpretations, on the one hand, and the Bohm interpretation, on the other. In the Bohm interpretation, the hidden variables are a part of physical reality. On the mind-based interpretations, the hidden variables are a part of mental reality. In all cases, we have at least partial access to the hidden variables.