ok, looking back through the historical results, overall wins in multiple classifications have been achieved numerous times.
The only rider to win overall, points and mountain titles in the one race was Mercx in 1969. He was also under 26 at the time so would have claimed the youth title if it had existed. This is the only time one rider has claimed both the mountain and points title.
Overall win and mountain title in the one race has been achieved 8 times - 1938 (Bartali), 1939 (Maes), 1948 (Bartali), 1949 & 1952 (Coppi), 1959 (Bahamontes), 1969 & 1970 (Mercx).
Overall win and points title in the one race has been achieved 4 times - 1969, 1971 & 1972 (Mercx), 1979 (Hinault)
Overall and youth title in the one race has been done 3 times - 1983 (Fignon), 1997 (Ullrich), 2007 (Contador)
Bear in mind the mountain competition only came into existance in 1933, points came in 1953 and youth in 1975 so give credit to the early doubles as they scored a clean sweep of all the titles available.
Looking at pre 1975 overall winners reveals 14 riders who would have also won the youth title if it had existed - Cornet (1904, youngest ever winner), Trousselier (1905), Petit-Breton (1907 & 1908), Faber (1909), Lapize (1910), Defraye (1912), Thys (1913, 1914), Maes (1935), Bartali (1938), Anquetil (1957), Gaul (1958), Gimondi (1965), Aimar (1966), Mercx (1969 & 1970).
Also, no post 1975 rider has claimed the youth title in conjunction with either the mountain or the points titles, however Bobet (1950) and Van Impe (1972) were the best placed U26 riders when they claimed their mountain titles. Mercx was also U26 when he took overall and mountain in 1970 and as such would have claimed the youth title if it had existed.
An interesting (but not unexpected) stat is that, excluding the youth titles, 1979 was the last time a rider claimed dual titles. One would assume this is because more specialists are competing for each title.
Yeah, I have a little spare time on my hands