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