I can't say as my knowledge of Chinese is limited, but it happens often when I'm seeking to check the pinyin transcription in my Chinese dictionary (it lists some 4,800 characters and 12,000 expressions). I just opened randomly at ōu and found 4 different ideograms for it, still randomly for huì and counted 14 ideograms, looked for mǎ and found 5, 3 for ráo, 8 for fǔ, 4 for cái, 5 for wū, 4 for tián ...
Either the dictionary has badly written the pinyin or as I have only learned basics, I may have missed some subtleties over the use of tones when it comes to written only language, but owing to random search over the entire dictionary and the findings of multiple characters with the same pinyin, making me supposing on probability grounds that it happens frequently (otherwise, it would have been very unlikely for me to find any just by opening any page randomly).
But just looking at the dictionary, with the table of possible pinyin vowels and consonants, we have some 759 possible pinyin syllabes (without distinction of tones), or 3795 with the 5 possible tones. Given the dictionary gives 4,800 characters, that gives a minimum 26% of pinyin syllabes having at least two different characters.
But that's over the sample of the dictionary and list of 56 pinyin consonants and vowels (23 and 33) it gives. As there exists much more Chinese characters (I read often that's around 50,000), even though you don't need much more to have fluent understanding, and surmising that there isn't much more possible pinyin syllabes than implied by the table of the dictionary, that gives an average 12 characters per pinyin syllabe. You'd then have to apply to that number the frequency of actual use for a given character to have an idea of the precise odd, surmising too that some pinyin are more used than others.
Now, that's a very mathematical approach, but you can guess why I'm so concerned with the monosyllabic system (on a mathematical point of view).