It is possible to define Scala case objects programmatically?

In my current project, I need to define a lot of case objects subclassing a single sealed trait. The names of these objects have a pattern, e.g., Case1, Case2, Case3, ..., CaseN. I was wondering if there is way in scala to define all these case objects in a programmatical way, for example with a loop, instead of writing N lines of definitions.

If this is feasible, it would also be great to do this at compile time so that the case objects defined in this way are known to type checking. This sounds impossible in most languages (you can have either dynamically defined types like in python or have static type safety like in C/C++, but not both), but maybe it is doable in Scala for its powerful compile-time reflection?