The max number of characters that map to a single pronunciation
The Phonology of Standard Chinese by San Duanmu (端木三) has a list of the 15 most common syllables, followed by the number of different characters pronounced that way, not including tones.
yi (106)，ji (93), yu (90),
fu (73),
zhi (72),
li (71),
qi (66),
yuan (64),
xi (64),
jian (61),
shi (58),
wu (55),
wei (53),
ju (51), pi (51）
Tones distribution should be roughly even for the most part  although the book does say that yi4 represents 63 different words.