  Type IIB S-folds of the form $\,\textrm{AdS}_{4} \times \textrm{S}^1 \times
\textrm{S}^5\,$ are conjectured to correspond to new strongly coupled
three-dimensional CFT's on a localised interface of $\,\textrm{SYM}_{4}\,$. In
this work we construct holographic RG flows on the D3-brane that generically
connect anisotropic deformations of $\,\textrm{SYM}_{4}\,$ in the UV to S-fold
$\textrm{CFT}$'s in the IR, the latter preserving various amounts of
supersymmetry as well as of residual symmetry. Examples of holographic RG flows
between S-fold CFT's are also presented. Lastly a geometric interpretation of
axion deformations is provided in terms of monodromies on the internal
$\,\textrm{S}^{5}\,$ when moving around the $\,\textrm{S}^{1}\,$. Special
attention is paid to the monodromy-induced patterns of symmetry breaking as
classified by the mapping torus $T_{h}(\textrm{S}^5)$.
