In this paper, we define Weyl--Ōtsuki spaces of the second kind and order $n$ (denoted $SW-O_n$) with a tensor $P$ in the form $P^i_s=S(x)\delta^i_s$, where $S(x)$ is a non-zero and non-linear $C^r$ $(r\geq3)$ function. We establish some relations between the curvature tensor and the conformal curvature-like tensor in $SW-O_n$ and analogous objects in an adjoint Riemannian space.