  We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical
generalised pairs exist, assuming the existence of minimal models of smooth
varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log
canonical generalised pair $ (X,B+M) $ we can run an MMP with scaling of an
ample divisor which terminates, assuming that it admits an NQC weak Zariski
decomposition or that $K_X+B+M$ is not pseudoeffective. As a consequence, we
establish several existence results for minimal models and Mori fibre spaces.
