Medium puzzles still lean on singles, but they'll stall you there at least once. You'll need locked candidates — when a digit's only possible cells in a box all sit in one row or column, it can be eliminated from the rest of that row or column — and naked pairs, where two cells in a unit share the same two candidates and rule those digits out everywhere else in the unit. Neither technique takes long to learn, and once it clicks you'll start seeing it everywhere.
Too easy? Easy is a step down. Want more of a fight? Hard is a step up.