We construct infinite new classes of AdS4 × S1 × S5 solutions of type IIB string theory which have non-trivial SL(2, ℤ) monodromy along the S1 direction. The solutions are supersymmetric and holographically dual, generically, to N = 1 SCFTs in d = 3. The solutions are first constructed as AdS4 × ℝ solutions in D = 5 SO(6) gauged supergravity and then uplifted to D = 10. Unlike the known AdS4 × ℝ S-fold solutions, there is no continuous symmetry associated with the ℝ direction. The solutions all arise as limiting cases of Janus solutions of d = 4, N = 4 SYM theory which are supported both by a different value of the coupling constant on either side of the interface, as well as by fermion and boson mass deformations. As special cases, the construction recovers three known S-fold constructions, preserving N = 1, 2 and 4 supersymmetry, as well as a recently constructed N = 1 AdS4 × S1 × S5 solution (not S-folded). We also present some novel “one-sided Janus” solutions that are non-singular.