Abstract: This work concerns the development of deep networks that are certifiably robust to adversarial attacks. Joint robust classification-detection was recently introduced as a certified defense mechanism, where adversarial examples are either correctly classified or assigned to the ``abstain'' class. In this work, we show that such a provable framework can be extended to networks with multiple explicit abstain classes, where the adversarial examples are adaptively assigned to those. While naively adding multiple abstain classes can lead to ``model degeneracy'', we propose a regularization approach and a training method to counter this degeneracy by promoting full use of the multiple abstain classes. Our experiments demonstrate that the proposed approach consistently achieves favorable standard vs. robust verified accuracy tradeoffs, outperforming state-of-the-art algorithms for various choices of number of detection classes.