This paper considers Proportional-Integral-Plus (PIP) control of nonlinear dynamic systems described by State Dependent Parameter (SDP) models with constraints. More specifically, a low level stabilising SDP/PIP controller is first developed to steer the system in the desired direction, whilst a Reference Governor (RG) is subsequently introduced to account for constraints in the system variables. This contrasts with the (off-line) simulation-based methods previously used for PIP control of SDP models with constraints. Furthermore, the particular parametrisation of the RG used in this paper provides useful insight into, and quantification of, the effects of the constraints on the nonlinear control system.