Collective action against algorithmic systems provides an opportunity for a small group of individuals to strategically manipulate their data to get specific outcomes, from classification to recommendation models. This effectiveness will invite more growth of this type of coordinated actions, both in the size and the number of distinct collectives. With a small group, however, coordination is key. Currently, there is no formal analysis of how coordination challenges within a collective can impact downstream outcomes, or how multiple collectives may affect each other's success. In this work, we aim to provide guarantees on the success of collective action in the presence of both coordination noise and multiple groups. Our insight is that data generated by either multiple collectives or by coordination noise can be viewed as originating from multiple data distributions. Using this framing, we derive bounds on the success of collective action. We conduct experiments to study the effects of noise on collective action. We find that sufficiently high levels of noise can reduce the success of collective action. In certain scenarios, large noise can sink a collective success rate from $100\%$ to just under $60\%$. We identify potential trade-offs between collective size and coordination noise; for example, a collective that is twice as big but with four times more noise experiencing worse outcomes than the smaller, more coordinated one. This work highlights the importance of understanding nuanced dynamics of strategic behavior in algorithmic systems.