Sleep stage dynamics can be adequately represented using Markov chain models to improve classification accuracy. The present study proposes a new post-processing method based on channel fusion using Latent Structure Influence Models (LSIMs). The proposed method develops and examines two channel-fusion algorithms: the standard LSIM fusion and the integrated LSIM fusion, in which the latter is more efficient and performs better. The proposed LSIM-based method simultaneously incorporates the nonlinear interactions between channels and the sleep stage dynamics. In the first step, existing sleep staging systems process every data channel independently and produce stage score sequences for each channel. These single-channel scores are then projected into belief space using the marginal one-slice parameter of all channels by LSIM fusion algorithms. The logarithms of marginal one-slice parameters are concatenated to obtain log-scale belief state space (LBSS) features in the standard LSIM fusion. In the integrated LSIM fusion, integrated LBSS (ILBSS) features are formed by combining the LBSS features of several LSIMs. By utilizing four recently developed sleep staging systems, the proposed method is applied to the publicly available SleepEDF-20 database that contains five AASM sleep stages (N1, N2, N3, REM, and W). Compared to single-channel (Fpz-Cz, Pz-Oz, and EOG) results, integrated LSIM fusion results have a statistically significant improvement of 1.5% in 2-channel fusion (Fpz-Cz and Pz-Oz) and 2.5% in 3-channel fusion (Fpz-Cz, Pz-Oz, and EOG). With an overall accuracy of 87.3% for 3-channel post-processing, the integrated LSIM fusion system offers one of the highest overall accuracy rates among existing studies.