Using the technique of dimensional reduction, we construct and study N=3 supersymmetric Maxwell Chern-Simons Higgs and Yang-Mills Chern-Simons Higgs models. By taking various limits of both theories, we also obtain a host of related reduced ones. Among them is the Yang-Mills Higgs theory whose supersymmetry turns out to be N=4, or even N=8 with certain matter multiplets. There is also a pure N=3 Yang-Mills Chern-Simons theory with an explicit O(3) symmetry. This completes the search for maximally supersymmetric theories with one gauge field and no gravity in 2+1 dimensions.
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