support has 49 distinct synonyms spread across 15 of its 22 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.
the activity of providing for or maintaining by supplying with money or necessities
“his support kept the family together”
aiding the cause or policy or interests of
“the president no longer has the support of his own party”
a military operation (often involving new supplies of men and materiel) to strengthen a military force or aid in the performance of its mission
“they called for artillery support”
documentary validation
“his documentation of the results was excellent”
the financial means whereby one lives
“each child was expected to pay for their keep”
supporting structure that holds up or provides a foundation
“the statue stood on a marble support”
the act of bearing the weight of or strengthening
“he leaned against the wall for support”
a musical part (vocal or instrumental) that supports or provides background for other musical parts
financial resources provided to make some project possible
“the foundation provided support for the experiment”
support with evidence or authority or make more certain or confirm
“The stories and claims were born out by the evidence”
play a subordinate role to (another performer)
“Olivier supported Gielgud beautifully in the second act”
Synonyms, antonyms and the broader and narrower relations for support come from Princeton University’s WordNet. Full sources and licences.