What if a law department took the 12-to-20 law firms it most commonly turns to and calculated the percentage of the firm’s revenue that comes from the department? You know your spend and you can estimate the firm’s revenue from league tables or extrapolations from them. If a firm has hundreds of lawyers, even a seven figure spend might be only a small part of its revenue – not much clout (See my post of Feb. 20, 2008: Latham & Watkins as $2 billion revenue.).
If you were being aggressive on cost control or other requirements, you can lean more on the law firms that depend on you the most. I have not heard of any law department that explicitly quantifies and exploits its leverage in such a way, but the concept may have applicability.