"The full amount expected, desired, or possible", Of unknown origin; the phrase is only recorded recently. Among various (unsubstantiated) theories, one cites the phrase the full Montague Burton, apparently meaning 'a complete three-piece suit' (from the name of a tailor of made-to-measure clothing in the early 20th century); another recounts the possibility of a military usage, the full monty being 'the full cooked English breakfast' insisted upon by Field Marshal Montgomery.
