get down has 26 distinct synonyms spread across 6 of its 7 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
lower (one's body) as by kneeling
“Get down on your knees!”
put down in writing; of texts, musical compositions, etc.
take the first step or steps in carrying out an action
“We began working at dawn”
Synonyms, antonyms and the broader and narrower relations for get down come from Princeton University’s WordNet. Full sources and licences.