  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-point
functions with analytic bootstrap methods. Relying on the results of a
companion paper for the kinematics and strong coupling spectrum, we consider
various four-point functions in the planar limit, in an expansion for large 't
Hooft coupling. Our ultimate goal is to provide a detailed derivation of the
four-point function of the displacement supermultiplet at three loops, first
presented in 2103.10440. Along the way, we present a large amount of new
results including four-point functions with zero, one or two long external
supermultiplets. The last two represent a novelty in the analytic bootstrap
literature and are instrumental in addressing the problem of operators
degeneracy. Such phenomenon leads to the necessity of resolving a mixing
problem that is more complicated than those usually encountered in the study of
holographic correlators, thus leading us to the development of a new approach
that we believe will have a wider range of applicability. Related to this
issue, we analyze in some detail the structure of the dilatation operator in
this model. Some of the ingredients that we use apply more generally to
holographic theories, although a thorough investigation of these aspects is
missing, to the best of our knowledge, in most interesting cases.
