  The phase diagram of the staggered six vertex, or body centered solid on
solid model, is investigated by transfer matrix and finite size scaling
techniques. The phase diagram contains a critical region, bounded by a
Kosterlitz-Thouless line, and a second order line describing a deconstruction
transition. In part of the phase diagram the deconstruction line and the
Kosterlitz-Thouless line approach each other without merging, while the
deconstruction changes its critical behaviour from Ising-like to a different
universality class. Our model has the same type of symmetries as some other
two-dimensional models, such as the fully frustrated XY model, and may be
important for understanding their phase behaviour. The thermal behaviour for
weak staggering is intricate. It may be relevant for the description of
surfaces of ionic crystals of CsCl structure.
