stand up has 10 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.
rise to one's feet
“The audience got up and applauded”
refuse to back down; remain solid under criticism or attack
put into an upright position
“Can you stand the bookshelf up?”
be standing; be upright
“We had to stand for the entire performance!”
resist or withstand wear, criticism, etc.
“Her shoes won't hold up”
Synonyms, antonyms and the broader and narrower relations for stand up come from Princeton University’s WordNet. Full sources and licences.