handle has 13 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.
be in charge of, act on, or dispose of
“I can deal with this crew of workers”
interact in a certain way
“Do right by her”
show and train
“The prize-winning poodle was handled by Mrs. Priscilla Prescott”
Synonyms, antonyms and the broader and narrower relations for handle come from Princeton University’s WordNet. Full sources and licences.