Why do ionic solids change to a structure with a higher coordination number at high pressures? This seems counter intuitive to me since ionic radius increases with increasing coordination number. Surely the solid doesn't expand under high pressure? Can you explain?
Lets put some numbers on the phase transition of NaCl from the normal NaCl structure (based on fcc, 6-fold coordinated) at atmospheric pressure, to the CsCl (based on bcc, 8-fold coordinated) structure at high pressure. 
From Compounds and Alloys Under High Pressure: A Handbook, by E. Yu Tonkov (google found it) one gets that the transition occurs at 27-29GPa, with a volume change of 5%.
The density of NaCl, taken from Wikipedia, is 2.165 gm/cc, or about 27cm$^3$/mol, or 27E-6 m$^3$/mol. 
Multiply on through and you get, very roughly, the PV energy gained by converting from the less dense NaCl structure to the denser CsCl structure is 40kJ/mol - this is not an inconsequential energy gain for the Gibbs free energy.  Thus, the PV energy gained by a denser solid with the higher coordination plays off (and pays off) against the ionic unhappiness.

In the literature there are also indications that the CsCl, and/or higher pressure phases, may be metallic in nature, so the assumption of purely ionic bonding may be in jeopardy.