Argumentation is fundamental for many learning assignments, ranging from primary school to university and beyond. Computer-supported argument scaffolds can facilitate argumentative discourse along with concomitant interactive discussions among learners in a group (i.e., first-order argument scaffolding). However, there is no evidence, and hence no knowledge, of whether such argument scaffolds can help students acquire argumentation competence that can be transferred by the students themselves to various similar learning tasks (i.e., second-order argument scaffolding). Therefore, this conceptual article argues that the focus of argument scaffold design and research should be expanded: from the study of first-order scaffolding alone to including the study of second-order scaffolding as well. On the basis of the Script Theory of Guidance (SToG), this paper presents a guideline for second-order argument scaffolding using diagnosis of the student’s internal argumentative script and offering adaptive external support and various fading mechanisms. It also explains how to complement adaptive fading support with peer assessment, automatic response tools, and adaptable self-assessment to ensure that learners actually understand, learn, and apply targeted argumentation activities in similar situations.