An easy way to discover sub-plots for your characters is to tell the story, in one or two paragraphs, from each of the main character’s point of view (don’t forget your antagonist). You’ll be amazed how bland their personalities were before you started this exercise.
Today, I did this for book 2 of my trilogy. Writing one paragraph from the four main characters point of views was easy but it showed that the two supporting characters didn’t have much of a part. Actually, it proved that they were quite boring. So I rewrote their paragraphs and looked at what was happening from deep within them and discovered some conflict. I saw sides of them that I didn’t know existed and now their parts in the overall story will have more meaning and the story will have more depth.
I’m yet to do this with two new characters. My hero’s brother will join us in book 2, and there is a new antagonist. I will learn a lot about them during this exercise.
Give it a try. I guarantee you’ll learn something new about your characters too.