  In this paper we construct compact manifolds with fixed boundary geometry
which admit Riemannian metrics of unit volume with arbitrarily large Steklov
spectral gap. We also study the effect of localized conformal deformations that
fix the boundary geometry. For instance, we prove that it is possible to make
the spectral gap arbitrarily large using conformal deformations which are
localized on domains of small measure, as long as the support of the
deformations contains and connects each component of the boundary.
