Characterizing semigroups $X$ with commutative extensions $varphi(X)$, $lambda(X)$, $N_2(X)$, $upsilon(X)$

We characterize semigroups $X$ whose semigroups of filters $varphi(X)$, maximal linked systems $lambda(X)$, linked upfamilies $N_2(X)$, and upfamilies $upsilon(X)$ are commutative.