The historical figure Plutarch?
The best I've been able to find is this (non-canonical) speculation from The Panem Companion. Its emphasis is on the origin of his name, but it includes some discussion of his background, career, and role in the story, so I thought it was interesting enough to merit an answer.
"Heavensbee" is a portmanteau and proprietary name. In southern vernacular, the phrase "Heavens be!" is a mild expression of surprise. But the name could also come from a line in the "Life of Pericles" (part of Parallel Lives), written by Heavensbee's namesake, the historical Plutarch:1
Diopeithes introduced a bill that those who did not recognise the gods, or who taught theories of the heavens, be prosecuted.
A Greek historian, biographer, essayist, and Platonic philosopher best known for his Parallel Lives and Moralia, the historical Plutarch was born to a Greek family under the name Ploutarchos, and was renamed upon becoming a Roman citizen. This may suggest that the Hunger Games' Plutarch came from somewhere outside the Capitol and took a Capitol name to avoid suspicion as he plotted the Second Rebellion;2 more likely, however, it is the historical Plutarch's work, not his background, that served as the inspiration for the Hunger Games' character.
The historical Plutarch focused most of his adult life on pointing out the moral deficiencies and inadequacies of Roman officials. [...] Plutarch was not concerned with the accurate recording of history so much as the influence of character, good or bad, on the lives and destinies of men.
Similarly, the Hunger Games' Plutarch worked to expose (and depose, in the case of Coriolanus Snow!) corrupt officials. He did this much in the same way the historical Plutarch did: just as Plutarch was interested in preserving and telling people's stories through popular writing (i.e., the Lives), Plutarch Heavensbee is interested in displaying and telling people's stories through reality TV programming (the Games, his proposed singing show).
1 OK, this bit is kinda far-fetched. But read on - the comparison with the historical figure Plutarch does sound interesting!
2 See this question: Where is Plutarch Heavensbee originally from?