We study the Kodaira dimension of almost complex manifolds admitting an \(\mathrm {SU} (m)\) -structure. We introduce the notion of almost complex structure of splitting type and of associated \(\mathrm {SU}(m)\) -structure. When the latter is pseudoholomorphic, we provide two constructions that allow to obtain non-invariant almost complex structures with Kodaira dimension 0, resp. with Kodaira dimension \(-\infty \) . Our results apply, in particular, to complex structures of splitting type and to several almost complex manifolds already well-studied in the literature.