  In this paper we expand a technique for differentiating higher Lie groupoids
that was initially outlined in previous work and has been elaborated in current
research. We extend this technique to the setting of general simplicial
manifolds. The concept underlying this extension is that even though simplicial
manifolds might not possess the additional criteria that characterize higher
Lie groupoids, they do satisfy "local Kan conditions", which suffices to
perform the constructions presented in the aforementioned study.
