You can do as many reaction rounds as your group wants to. Doing two rounds is not unusual at all. More than two rounds, in our experience often doesn’t lead to more insight. If there is a need for an additional round, it’s often very effective to give a slightly new prompt, for example, to sharpen the focus on one controversial issue, or to ask for reactions to one particular aspect or to think about what could be a next step.
For more information, check out our handbook Many Voices One Song section 5.5