A (possibly new) structure without the canonical base property

In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new uncountably categorical additive covers of the complex numbers without the canonical base property.
Comment: Added: Elimination of finite imaginaries in a cover of a group of Lascar rank one yields a connection to the canonical base property