Educational technologies are often developed such that students work on specific social levels (e.g., individual, small group, whole class) at specific times. However, in the reality of the classroom, learning activities are not so cleanly divided, with transitions occurring between social levels for students at different times. To support these social transitions in a way that can promote student learning, we need to lower the teacher's orchestration load around managing fluid social transitions. Co-orchestration, in which the orchestration decisions are shared between different parties, can help to lower the orchestration load when it is designed according to the teacher's values and classroom culture. In this paper, we present a taxonomy of social transitions and investigate how the responsibilities of orchestration can be divided between primary school teachers and a co-orchestration system in order to support the extension from rigid social transitions to fluid transitions in technology-enhanced classrooms. Across two studies, we used a design process involving co-design and prototyping with teachers. We uncovered and refined co-orchestration design desires that balance teachers' orchestration loads while providing them with a sense of control. We present six design desires for maintaining a balance between teacher and system responsibilities regarding the orchestration of social transitions that can be implemented, such as in our mid-fidelity prototype, to support the range of social transitions. The list of desires contributes to co-orchestration research and more broadly technology design for classrooms by highlighting the changing balance of teacher control depending on what is the focus of the orchestration support.