  Motivation:
  In systems biology, modelling strategies aim to decode how molecular
components interact to generate dynamical behaviour. Boolean modelling is more
and more used, but the description of the dynamics from two-levels components
may be too limited to capture certain dynamical properties. %However, in
Boolean models, the description of the dynamics may be too limited to capture
certain dynamical properties. Multivalued logical models can overcome this
limitation by allowing more than two levels for each component. However,
multivaluing a Boolean model is challenging.
  Results: We present MRBM, a method for efficiently identifying the components
of a Boolean model to be multivalued in order to capture specific fixed-point
reachabilities in the asynchronous dynamics. To this goal, we defined a new
updating scheme locating reachability properties in the most permissive
dynamics. MRBM is supported by mathematical demonstrations and illustrated on a
toy model and on two models of stem cell differentiation.
