That has nothing to do with dependency injection
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You can specify the base class of an entity type btw. As long as that class inherits from EntityBase (selfservicing) or EntityBase2 (adapter). You can do that in the project properties, Output setting values: EntityBaseClassNameDefault. You can specify a macro there, i.e. {$Name} to get it replaced at generation time with the entity name, e.g. {$Name}Base, will become for the entity Customer: CustomerBase.
Now, what you can do is this: Your domain project contains classes, one for each entity, e.g. CustomerBase. These classes inherit from EntityBase or EntityBase2. They're all abstract. In these classes you define the domain logic. Make sure the constructors are properly called. Define these as protected. It's key you have the same constructors as CommonEntityBase. In the designer you define the default for the entitybaseclass name, as described above. This will cause the generator to define the base class for each entity to be {$Name}Base, e.g. for Customer the base class will be CustomerBase. You now reference the domain project from the generated code and everything should compile.
However you can also look at seeing domain logic more as a service, as often domain logic affects multiple entities, so spreading that across multiple entities is not that useful.