The field of abduction is multifaceted, and views on it are diverse. Today, it seems clear that different forms of abductive cognition have to be distinguished. Yet, some such forms have perhaps unduly been labeled “abductive”, so that one important task is to determine the very point of abduction, while another is to differentiate and integrate the remaining forms of abduction in a system of abductive (and non-abductive) inferences. The present contribution builds on the rich and possibly exhausting array of forms of abduction that have been suggested by Lorenzo Magnani in his ingenious and most inspiring project of capturing and broadening the scope of abductive cognition. His eco-cognitive model of cognition is fully endorsed, as is the relevance of the various forms of abduction that Magnani has brought to the fore. However, some of the concepts he has posited deserve a closer look regarding their precise status and their overall connections. The present contribution suggests a taxonomical frame of reference for addressing forms of inferential cognition in general and abduction in particular, and discusses Magnanian concepts in its context, with a particular focus on Magnani’s “manipulative” abduction, which is held to be, in fact, a case of Peirce’s “theorematic deduction”.