  We present a theoretical description of the effect of polyvalent ions on the
interaction between titratable macro-ions. The model system consists of two
point-like macro-ions with dissociable sites, immersed in an asymmetric ionic
mixture of monovalent and polyvalent salts. We formulate a {\em dressed ion
strong coupling theory}, based on the decomposition of the asymmetric ionic
mixture into a weakly electrostatically coupled monovalent salt, and into
polyvalent ions that are strongly electrostatically coupled to the titratable
macro-ions. The charge of the macroions is not considered as fixed, but is
allowed to respond to local bathing solution parameters (electrostatic
potential, $pH$ of the solution, salt concentration) through a simple {\em
charge regulation} model. The approach presented, yielding an effective
polyvalent-ion mediated interaction between charge-regulated macro-ions at
various solution conditions, describes the strong coupling equivalent of the
Kirkwood-Schumaker interaction.
