We use simple acid-base chemistry to control the valency in self-assembled monolayers of two different carboranedithiol isomers on Au{111}. Monolayer formation proceeds via Au-S bonding, where manipulation of pH prior to or during deposition enables the assembly of dithiolate species, monothiol/monothiolate species, or combination. Scanning tunneling microscopy (STM) images identify two distinct binding modes in each unmodified monolayer, where simultaneous spectroscopic imaging confirms different dipole offsets for each binding mode. Density functional theory calculations and STM image simulations yield detailed understanding of molecular chemisorption modes and their relation with the STM images, including inverted contrast with respect to the geometric differences found for one isomer. Deposition conditions are modified with controlled equivalents of either acid or base, where the coordination of the molecules in the monolayers is controlled by protonating or deprotonating the second thiol/thiolate on each molecule. This control can be exercised during deposition to change the valency of the molecules in the monolayers, a process that we affectionately refer to as the "can-can." This control enables us to vary the density of molecule-substrate bonds by a factor of 2 without changing the molecular density of the monolayer.