I ask this question because I had wrongly described Old Mars as presenting fifteen original versions of Mars. In fact:
SM Stirling's "Swords of Zar-tu-Kan" is a prequel to the same author's Mars novel;
Matthew Hughes' "The Ugly Duckling" is a sequel to Ray Bradbury's The Martian Chronicles, which is itself a series;
there might be similar surprises in store in the remaining contents of the anthology.
Edwin Arnold's Lieut. Gulliver Jones, a possible source for ERB's A Princess Of Mars, ends, like Wells' The First Men In The Moon, in a way that rules out a sequel. The magic rug returns Jones to Earth, then disappears forever. However, A Princess... became a series that inspired further, imitative, series by both Otis Adelbert Kline and Michael Moorcock.
So we have identified Martian series by Anderson, Stirling, Bradbury, Burroughs, Kline and Moorcock. There are other such series on the periphery of my awareness. Poul Anderson is much better known for his many other kinds of writing but it is good to see that, with just two short stories, he does make it onto the list of authors of Martian series.