There weren't parts one or two, but this title clearly has meaning. Perhaps they were classified, like Leonard parts 1-5?
Like a lot of other shows (like the Simpsons, for instance), Frasier's episode titles were sometimes puns or allusions to movies, shows, books and other pop culture references. This episode's title, according to TV.com, is alluding to Tony Kushner's famous play Angels in America, which 2 parts premiered separately in 1991 and 1992 (the episode is from 1995):
Episode Title: Agents in America, Part III
A reference to the two-part play Angels in America (hence the "Part III" in the title).
It's also worth noting that it's possibly 'Part III' as this is the 3rd episode with Frasier's agent Bebe (follwing Selling Out and And the Whimper Is...). I don't think there's much of a connection between the plot of this episode and Angels in America (maybe Bebe's machinations could be compared to Roy Cohn's shady dealings, but that's a stretch), so it's probably just a pun and nothing more.