Very often time series are subject to abrupt changes in the level, which are generally represented by Markov Switching (MS) models, hypothesizing that the level is constant within a certain state (regime). This is not a realistic framework because in the same regime the level could change with minor jumps with respect to a change of state; this is a typical situation in many economic time series, such as the Gross Domestic Product or the volatility of financial markets. We propose to make the state flexible, introducing a very general model which provides oscillations of the level of the time series within each state of the MS model; these movements are driven by a forcing variable. The flexibility of the model allows for consideration of extreme jumps in a parsimonious way (also in the simplest 2-state case), without the adoption of a larger number of regimes; moreover this model increases the interpretability and fitting of the data with respect to the analogous MS model. This approach can be applied in several fields, also using unobservable data. We show its advantages in three distinct applications, involving macroeconomic variables, volatilities of financial markets and conditional correlations.