  We consider the classical geometric problem of prescribing the scalar and
boundary mean curvatures via conformal deformation of the metric on a
$n-$dimensional compact Riemannian manifold. We deal with the case of negative
scalar curvature and positive boundary mean curvature. It is known that if
$n=3$ all the blow-up points are isolated and simple. In this work we prove
that, for a linear perturbation, this is not true anymore in low dimensions
$4\leq n\leq 7$. In particular, we construct a solution with a clustering
blow-up boundary point (i.e. non-isolated), which is non-umbilic and is a local
minimizer of the norm of the trace-free second fundamental form of the
boundary.
