The purpose of this paper is to show how microargumentation mechanisms of presumptive reasoning and reasoning from best explanation can be used to explain some cases of presupposition suspension. It will be shown how the relationship between presupposition triggers and pragmatic presuppositions can be analyzed in terms of presumptive and nonpresumptive polyphonic articulation of an utterance, resulting in different types of commitments for the interlocutors. This approach is grounded on the two interconnected notions of presumptions and commitments. In some complex cases of presupposition suspension, the speaker presumes the hearer s acceptance of, and commitment to, propositions that do not belong to the common ground or that have been explicitly rejected as being commonly shared. This phenomenon triggers a complex type of reasoning that can be represented as kind of abduction, grounded on hierarchies of presumptions and aimed at providing an interpretation that solves this conflict of presumptions. Several cases of presupposition suspension will be shown to result from nonpresumptive polyphonic articulations, in which different voices responsible for distinct commitments are distinguished. By indirectly reporting an element of discourse, the speaker can refuse to take responsibility for the presupposed proposition, and correct the commitments that may result for him or her. This polyphonic treatment of utterances can explain how and why a presupposition is suspended, and can be used to identify the conflicting presumptions that can be further solved through reasoning from best explanation. This reasoning can result in a different reconstruction of the developed logical form or the illocutionary force of an utterance.