manipulate has 11 distinct synonyms spread across 4 of its 6 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.
influence or control shrewdly or deviously
“He manipulated public opinion in his favor”
maintain influence over (others or oneself) skillfully, usually to one's advantage
“She manipulates her boss”
treat manually, as with massage, for therapeutic purposed
Synonyms, antonyms and the broader and narrower relations for manipulate come from Princeton University’s WordNet. Full sources and licences.