For some reason, Apple only allows you to have three fingerprints saved to your Mac, as opposed to the five entries allowed on Touch ID iPhones. While there’s no way to add more individual fingerprints to your account, there is a way to double the number of fingerprints that will work to unlock the machine.
When scanning your fingerprint from System Preferences > Touch ID, use one finger until you see “Keep going to capture the edges of your fingerprint.” Now, switch to another finger, and complete the scan. It seems silly, but that one scan now recognizes both fingerprints. If you use this method for all three entires, your Mac will recognize six different fingerprints.