A general counsel might agree to provide to a primary law firm the department’s historical data on some class of matters. The only data redacted would be the name of the law firm that handled the matter (and any identifying information about timekeepers and rates). Thus the firm would be able to analyze cycle times, monthly billing, milestones, staffing and other factors that drive costs.
As a first step, the firm entrusted with this ore might figure out the cost parameters of those kinds of matters. As a consequence, the firm might be much more willing and able to offer to handle upcoming matters for a fixed fee, since its partners would know much about them possibly more than the law department. As a third benefit, the insights would help the firm attract other clients or prospects. They could speak knowledgably about drivers of costs.
Oh, and the law firm should not charge for this privileged access to information and insights and the excavations they conduct.