How large are we talking about for these grain haulers?
There are no surviving examples, but the Caligula (third emperor) had columns quarried in Egypt for a temple, each one of those ran about 200 tons. The largest of the obelisks now in Rome was likewise brought during Caligula's reign, and exceeds 300 tons; that ship was so large that it was kept around as a tourist attraction. The bread dole in Rome supported at least a couple hundred thousand for at least a few centuries, with peak years of about 400,000, so there must have been a good-sized fleet of grain ships for that and for the rest of the million or so residents of the city. Casson estimated 100 tons for the grain ships, but they probably much larger than that.