I don’t think any author begins thinking serious about writing a series novel. That comes only after he/she has produced at least one book with possibilities to extend. When thinking about what a character would do or say one is building a personality that may continue to exist even though such presence is no longer a part of the last novel. That is to say, a developed character usually has a future beyond the current version of the story. And that’s what a series novel does: explores the future.

Now something basic. To provide continuity, the author should make sense of the geographic location in the past book. Continuity is lost with a completely new location. Of course you can change locations, but that requires careful resetting of the ambiance. In my Rabbi Gabrielle stories I had her leave the US and do work in Israel. She stayed there for the entire novel, then in the newest (Book 6) Rabbi Gabrielle Hatches a Scheme she moves over the Israeli frontier into the Palestinian West Bank. That’s a credible geographic move which doesn’t require leaving all her old buddies back in Israel proper. But moving her to New York, or London, why that would require substantial restaging of people and local.