deep has 14 distinct synonyms spread across 8 of its 21 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. Its one recorded opposite is shallow.
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.
relatively deep or strong; affecting one deeply
“a deep breath”
having great spatial extension or penetration downward or inward from an outer surface or backward or laterally or outward from a center; sometimes used in combination
“a deep well”
of an obscure nature
“the new insurance policy is written without cryptic or mysterious terms”
9 of the 21 recorded senses carry no synonym, antonym or related term, so they are not shown above. Every sense, with its definition and examples, is on the full entry for deep.
Synonyms, antonyms and the broader and narrower relations for deep come from Princeton University’s WordNet. Full sources and licences.