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In this second installment of a series of two papers on the$\tfrac{1}{2}$-BPS Wilson line defect CFT in $\mathcal{N}=4$ super Yang-Mills,we focus on dynamical aspects of the theory, in particular studying four-pointfunctions with analytic bootstrap methods. Relying on the results of acompanion paper for the kinematics and strong coupling spectrum, we considervarious four-point functions in the planar limit, in an expansion for large 'tHooft coupling. Our ultimate goal is to provide a detailed derivation of thefour-point function of the displacement supermultiplet at three loops, firstpresented in 2103.10440. Along the way, we present a large amount of newresults including four-point functions with zero, one or two long externalsupermultiplets. The last two represent a novelty in the analytic bootstrapliterature and are instrumental in addressing the problem of operatorsdegeneracy. Such phenomenon leads to the necessity of resolving a mixingproblem that is more complicated than those usually encountered in the study ofholographic correlators, thus leading us to the development of a new approachthat we believe will have a wider range of applicability. Related to thisissue, we analyze in some detail the structure of the dilatation operator inthis model. Some of the ingredients that we use apply more generally toholographic theories, although a thorough investigation of these aspects ismissing, to the best of our knowledge, in most interesting cases.

Unmixing the Wilson line defect CFT. Part II: analytic bootstrap