Abstract: This paper introduces a new class of Markov switching models where switches in variables are not perfectly correlated. Maximum-likelihood estimates of the parameters are derived and shown to require only the smoothed inferences obtained from a univariate analysis of the variables. The framework is used to estimate a multiple Markov switching (MMS) model of South African financial and economic variables, which can be used for various actuarial applications, especially those involving long-term projections. Users may wish to set certain parameters in relation to future expectations rather than simply using estimates based on past data, but that process is not covered in this paper.