  In this paper we deepen the analysis of certain classes M_{g,k} of hyperbolic
3-manifolds that were introduced in a previous work by B. Martelli, C. Petronio
and the author. Each element of M_{g,k} is an oriented complete finite-volume
hyperbolic 3-manifold with compact connected geodesic boundary of genus g and k
cusps. We study small deformations of the complete hyperbolic structure of
manifolds in M_{g,k} via a close analysis of their geodesic triangulations. We
prove that several elements in M_{g,k} admit non-homeomorphic hyperbolic Dehn
fillings sharing the same volume, homology, cusp volume, cusp shape, Heegaard
genus, complex length of the shortest geodesic, length of the shortest return
path, and Turaev-Viro invariants. Manifolds which share all these invariants
are called geometrically similar, and were first studied by C. D. Hodgson, R.
G. Meyerhoff and J. R. Weeks. The examples of geometrically similar manifolds
they described are commensurable with each other. We show here that many
elements in M_{g,k} admit non-commensurable geometrically similar Dehn
fillings.
  The notion of geometric isolation for cusps in a hyperbolic 3-manifold was
introduced by W. D. Neumann and A. W. Reid and studied by D. Calegary, who
provided explanations for all the previously known examples of isolation
phenomena. We show here that the cusps of any manifold M_{g,k} are
geometrically isolated from each other. Apparently, isolation of cusps in our
examples arises for different reasons from those described by Calegari.
  We also show that any element in M_{g,k} admits an infinite family of
hyperbolic Dehn fillings inducing non-trivial deformations of the hyperbolic
structure on the geodesic boundary.
