The compound 'three-way' is a transparent Modern English formation, directly combining the numeral 'three' and the noun 'way'. Its constituent roots trace back to deep Indo-European ancestry: 'three' originates from the Proto-Indo-European root trei-, which yielded the numeral across many language families, including Latin tres and Greek treis. 'Way' derives from the Proto-Indo-European weǵʰ- meaning 'to transport or go', which evolved into concepts of road and journey. The logic of the compound is purely descriptive, fusing the ancient concept of the number three with the ancient concept of a path to denote anything involving three directions, participants, or branches, reflecting a straightforward method of English word formation.

Structure: three (number) + way (path/direction) - three: From Old English þrīe, þrēo, of Germanic origin; related to Dutch drie and German drei, from an Indo-European root shared by Latin tres and Greek treis. Functions as a numerical root. - way: From Old English weg, of Germanic origin; related to Dutch weg and German Weg, from an Indo-European root shared by Latin via 'road'. Functions as a noun root meaning a path, course, or manner.