  We propose and perform a joint analysis of the two different mass estimates
of galaxy clusters, namely the hydrostatic and caustic techniques. Firstly, 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, allow 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 screening and Vainshtein screening.
As anticipated, we show that the joint analysis can help improve the
constraints on these modified gravity scenarios.
