  Non-invertible symmetries have recently been understood to provide
interesting contraints on RG flows of QFTs. In this work, we show how
non-invertible symmetries can also be used to generate entirely new RG flows,
by means of so-called "non-invertible twisted compactification". We illustrate
the idea in the example of twisted compactifications of 4d $\mathcal{N}=4$
super-Yang-Mills (SYM) to three dimensions. After giving a catalogue of
non-invertible symmetries descending from Montonen-Olive duality
transformations of 4d $\mathcal{N}=4$ SYM, we show that twisted
compactification by non-invertible symmetries can be used to obtain 3d
$\mathcal{N}=6$ theories which appear otherwise unreachable if one restricts to
twists by invertible symmetries.
