plan has 7 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.
have the will and intention to carry out some action
“He plans to be in graduate school next year”
make a design of; plan out in systematic, often graphic form
“design a better mousetrap”
a series of steps to be carried out or goals to be accomplished
“they drew up a six-step plan”
an arrangement scheme
“the awkward design of the keyboard made operation difficult”
scale drawing of a structure
“the plans for City Hall were on file”
Synonyms, antonyms and the broader and narrower relations for plan come from Princeton University’s WordNet. Full sources and licences.