One generalises the notion of stabilizing bisets from [BouThe] to n-stabilizing bisets. This allows us to find new examples of stabilization for Roquette groups. We first investigate the idea of n-stabilizing bisets. We give a way to construct examples with the notion of idempotent bisets and n-expansive subgroups. Finally, for example, we look at Roquette groups and classify their n-stabilizing bisets.