'many-veined' is a Modern English compound formed from 'many' + 'veined'. 'many' ultimately comes from Old English 'manig' (meaning 'many, much'), and 'veined' is the past-participle/adjectival form of 'vein', from Old French 'veine' and Latin 'vena' meaning 'vein (blood vessel)'.

The element 'vein' derives from Latin 'vena' → Old French 'veine' → Middle English 'vein'. The adjectival form 'veined' developed in Middle to Early Modern English; combining it with 'many' produced the descriptive compound 'many-veined' in Modern English usage.

Originally a literal description meaning 'having many veins', the compound has retained that basic physical sense and is chiefly used in botanical and entomological contexts to describe structures with numerous veins.