For the writer, a series requires timeline and character analysis sheets. All of these characters are floating around, having children, dying, leaving, arriving, and it's easy to lose track especially for books that go over a period of many years. Readers keep track of the details; so the writer better be sure they don't blow it.
The other must for me is that I like the characters enough to stick around for more of their lives. A reader will be in a book for a few hours or days. When I write one, especially the historicals, I am in it for months. I don't do that unless I really enjoy the hero and heroine and often the secondary characters that add flavor.
In my Oregon series, the first book was in 1851 at the onset of the Oregon Trail. When I wrote it, I saw it as a stand-alone. It is the story of the Oregon Trail, two families and the growth of not only a love story but of two young people through what they experienced. It was only many years later that I thought-- what about the guy who lost out on the girl? In many ways, he was more the stereotypical hero than the hero who won her love. Who would he love?
Series are born out of such ideas and a desire to know-- what comes next?
The Oregon series moved from one setting to another. Some series writers set their books in a community and not only does time not change so much but neither does the setting. Readers there get used to knowing how the towns are set up and who owns the ranches.
The Oregon series went from 1851 to 1866 with some skips in time and then back into a new romance. With four books out, there are several more ideas for future stories that would tell more of the Oregon story as well as romances. If I write them, they will be helped by my knowing these characters. The drawback for moving too far in the future is some of the characters will have to die of old age. That is life but not sure I am ready for it in my Oregon historical series.
I did some looking around for articles on the series for any writers who might be thinking of doing one.
In my contemporary romances, I often have connecting characters, but I don't consider something a series unless it is 3 or more.