We introduce a class of four dimensional field theories constructed by quotienting ordinary N=4 U(N) SYM by particular combinations of R-symmetry and SL(2,Z) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order

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... These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS_5× (S^5/Z_k). Upon reduction on a circle the N=3 theories flow to well-known N=6 ABJM theories.