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Given an NQC log canonical generalized pair $(X,B+M)$ whose underlyingvariety $X$ is not necessarily $\mathbb{Q}$-factorial, we show that one may runa $(K_X+B+M)$-MMP with scaling of an ample divisor which terminates, providedthat $(X,B+M)$ has a minimal model in a weaker sense or that $K_X+B+M$ is notpseudo-effective. We also prove the existence of minimal models ofpseudo-effective NQC log canonical generalized pairs under various additionalassumptions, for instance, when the boundary contains an ample divisor.

Remarks on the existence of minimal models of log canonical generalized pairs