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Developed for complex systems undergoing rare events involving many (meta)stable states, the multiple state transition path sampling aims to sample from an extended path ensemble including all possible trajectories between any pair of (meta)stable states. The key issue for an efficient sampling of the path space in this extended ensemble is sufficient switching between different types of trajectories. When some transitions are much more likely than others the collective sampling of the different path types can become difficult. Here we introduce a Wang-Landau based biasing approach to improve the sampling. We find that the biasing of the multiple state path ensemble does not influence the switching behavior, but does improve the sampling and thus the quality of the individual path ensembles.