WordNet records no synonym and no antonym for hold one's own. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
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.
maintain one's position and be in control of a situation
1 of the 2 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for hold one's own.
Synonyms, antonyms and the broader and narrower relations for hold one's own come from Princeton University’s WordNet. Full sources and licences.