We construct a continuous one parameter family of $AdS_4times S^1times S^5$ S-fold solutions of type IIB string theory which have nontrivial $SL(2,mathbb{Z})$ monodromy in the $S^1$ direction. The solutions span a subset of a conformal manifold that contains the known $mathcal{N}=4$ S-fold SCFT in $d=3$, and generically preserve $mathcal{N}=2$ supersymmetry. We also construct RG flows across dimensions, from $AdS_5times S^5$, dual to $mathcal{N}=4$, $d=4$ SYM compactified with a twisted spatial circle, to various $AdS_4times S^1times S^5$ S-fold solutions, dual to $d=3$ SCFTs. We construct additional flows between the $AdS_5$ dual of the Leigh-Strassler SCFT and an $mathcal{N}=2$ S-fold as well as RG flows between various S-folds.
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