We propose and perform a joint analysis of the two different mass estimates of galaxy clusters, namely, the hydrostatic and caustic techniques. First, we show comprehensively that the mass bias between these two techniques can be possibly alleviated when cluster-specific assumptions constrained using the hydrostatic technique are utilized within the caustic technique. While at face value this demotes the caustic technique from a completely independent method, this allows one to further tighten the constraints on the cluster mass and, subsequently, allows us to test modifications to gravity. Implementing the aforementioned formalism for two well-observed massive galaxy clusters, A2029 and A2142, we highlight the proof of concept. In the current implementation, we use this method to constrain the chameleon and Vainshtein screening. As anticipated, we show that the joint analysis can help improve the constraints on these modified gravity scenarios.
