  Leggett-Garg inequalities are tests of macroscopic realism that can be
violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg
tests on a three-level system and implement measurements that admit three
distinct measurement outcomes, rather than the usual two. In this way we obtain
violations of three- and four-time Leggett-Garg inequalities that are
significantly in excess of those obtainable in standard Leggett-Garg tests. We
also report violations the quantum-witness equality up to the maximum permitted
for a three-outcome measurement. Our results highlight differences between
spatial and temporal correlations in quantum mechanics.
