Variant of Zilber-Pink for weakly special subvarieties

Let $V'\subsetneq\Gamma\backslash X^+$ be an irreducible subvariety, and let $ZP_{V',W}$ denote the union of the atypical intersection components defined in the paper using $WS_{\Gamma\backslash X^+}(M,X_M,x)$. Variant of Zilber-Pink for weakly special subvarieties. There exist $Z_1,\ldots,Z_k\in WS_{\Gamma\backslash X^+}(M,X_M,x)$ such that

$$ZP_{V',W}\subseteq Z_1\cup\cdots\cup Z_k\neq\Gamma\backslash X^+.$$

This is presented as the weakly special formulation equivalent to the relevant Zilber–Pink conjecture; the source gives no resolution.