Instruction often spans multiple phases (e.g., phases of discovery learning, instructional explanations, practice) with different learning goals and different pedagogies. For any combination of multiple phases, we use the term composite instructional design (CID). To understand the mechanisms underlying composite instructional designs, we propose a framework that links three levels (knowledge, learning, instruction) across multiple phases: Its core element is the specification of learning mechanisms that explain how intermediate knowledge (i.e., the knowledge state between instructional phases) generated by the learning processes of one phase impacts the learning processes of a following phase. The CID framework serves as a basis for conducting research on composite instructional designs based on a cognitive analysis, which we exemplify by discussing existing research in light of the framework. We discuss how the CID framework supports understanding of the effects of composite instructional designs beyond the individual effects of the single phases through an analysis of effects on intermediate knowledge (i.e., the knowledge state resulting from a first instructional phase) and how it alters the learning processes initiated by the instructional design of a second phase. We also aim to illustrate how CID can help resolve contradictory findings of prior studies (e.g., studies that did or did not find beneficial effects of problem solving prior to instruction). Methodologically, we highlight the challenge of altering one learning mechanism at a time as experimental variations on the instructional design level often affect multiple learning processes across phases.