Model structure induced by a combinatorial model category.

In Hirschhorn's Model categories and their localizations he gives a sufficient condition to induce a cofibrantly generated model structure on a category $\mathcal{N}$, given an adjoint pair of morphisms $\mathcal{F:M\rightleftarrows N:U}$ (where $\mathcal{M}$ is a cofibrantly generated model category) such that the adjoint functors induce a Quillen equivalence. Using Kan's characterisation of cofibrantly generated model categories.

Is there a way to make a similar statement about combinatorial model categories along the lines of Jeff Smith's theorem?

My main motivation for this is to see whether I can use the diagonal functor from the category of $n$-simplicial sets to the category of simplicial sets to define a combinatorial model structure on $n$-simplicial sets.