It's popular to write a series of books using the same main character. Often this happens accidentally when an author writes about a character who is so engaging that readers beg for more. Other authors plan to write a series from the beginning.
If you think you may want to develop one book into a series, it's important to plan ahead to ensure the backstory is deep enough to accommodate more than one book. Here are some points to consider before you write a series of mysteries:
1. Main character development: Develop a full biography of your main character including many idiosyncrasies and details about his/her childhood, youth, and early working years. You may not need all of it in your first book, but over time, you will draw on the details in your character's biography time and time again.
2. Secondary characters: If you are writing a series of books, it'll add to the depth of your story and the enjoyment of your readers if you have a small cast of recurring secondary characters for your main character to interact with.
Backstory development for each of these secondary characters is important to give your characters consistency from one book to the next. Readers like the predictability of these details and they often come back to read subsequent books due to the quirks of secondary characters as well as the appeal of your main character.
3. Setting: Unless your character will be in a different location for each book of your series, you will need to spend a bit of concentrated time developing the overall setting and several familiar settings within the area. I'll go into this in more detail later. For now, give the main setting and sub-settings some thought. Be sure to choose locations that will accommodate your main character, his/her type of mystery business, lifestyle and friends.
For example, if you want to develop a series about a bookish, middle-age woman who just happens to have dead bodies fall at her feet, such as Jessica Fletcher, a small town setting would probably work best. However, if your main character is a police detective, a big city setting might be better.
Before you write, it's important to give the setting considerable thought so it will work best for not only the first book but for subsequent books in the series.
You will write from greater authenticity if you develop the details about your main and secondary characters and your setting fully before your write your book. Rather than making up details later, you will have them at hand. Doing this detail work before you write will ensure the consistency and accuracy that readers demand.