Complex meaningful processes are thought to be constructed from elementary smaller ones that may be subjected to additional impacts. A principled theory defining the elementary processes, however, is still lacking. Consequently, theoretical formulations of how elementary processes and potential impacts operating (upon) them jointly create composite processes are mostly suitable to particular instances only. Here, we build on recent insights that elementary processes (named functional modes) can be distinguished through their topological structure in phase space. Certain modes may function independently, but others require external impacts operating (on) them (named operational signals). We illustrate how different functional architectures may construct complex processes utilizing distinct functional modes and operational signals in the context of a composite movement. Architectures differ from one another in terms of the time scale of the associated modes and operational signals. Different external operation is required for architectures that are dissimilar in their functional modes’ complexity. We reveal a tradeoff between the modes’ complexity and degree of external operation required, which is interpretable in terms of control and/or effort demands. Our result provides a theoretical basis for the construction of complex processes from elementary ones, with implications for learning, rehabilitation, robotics, and man-machine interfaces.