Smartthings has two different kinds of modes.
Location.modes are for things like daytime and night time and you can add more of those. They can be used to control when automations run.
However, security.modes are for the SmartThings home monitor ( in the new V3 app) Or smart home monitor (in the classic V2 app). Those control the security features and you cannot add any more of those, you are just stuck with the three that they give you.
It’s easy to get confused about these because they both have a value of “home“ and “away“ but they are used in quite different ways.
The following thread has examples of how each type of mode is used and usually helps clear up the confusion between them.
FAQ: Armed/Disarmed states vs Away/Home modes confusion (Classic app)
So the answer is, it depends on which type of modes you are talking about. If it’s the ones associated with SmartThings home monitor, that’s the security.mode, and you can’t add additional ones.