The development of nonlinear representations and of generalized IRFs favored the study of the variables behavior in response to an economically identified shock as regards (i) the state of the system when the shock occurs, (ii) the size of the shock and (iii) the sign of the shock. Generalized IRFs are widely used in threshold representations to illustrate and even test the presence of asymmetries (Potter, 1995, van Dijk et al., 2007). However, GIRF have known no comparable development in Markov-switching VAR. I show that whether IRF and GIRF recently developed in this framework impose sign and size symmetries or display poor properties. In this paper, I propose a new GIRF for general Markov-switching structural VAR with fixed transition probabilities. In a simulation framework inspired from Rubio-Ramirez et al. (2005), I relax the assumption of perfect knowledge of the regime and introduce the updating step proposed by Camacho and Perez-Quiros (2013). As a consequence, sign/size asymmetries can now be examined in MSIAH-VAR and the GIRF now incorporates the dependence on future shocks without extra complexity. Visited regimes can now differ endogenously between the shocked and baseline trajectories due to the initial and future shocks but the only exogenous difference in the simulated trajectories relies on the initial structural shock. I use this approach to implement a test for sign and size asymmetries on US aggregate gross job flows.