Large-scale pressure buildup in response to carbon dioxide (CO2) injection in the subsurface may limit the dynamic storage capacity of suitable formations, because elevated pressure can impact caprock integrity, induce reactivation of critically stressed faults, drive CO2 and/or brine through conductive features into shallow groundwater resources, or may affect existing subsurface activities such as oil and gas production. It has been suggested that pressure management involving the extraction of native fluids from storage formations can be used to control subsurface pressure increases caused by CO2 injection and storage, thereby limiting the possibility of unwanted effects. In this study, we introduce the concept of “impact-driven pressure management (IDPM),” which involves optimization of fluid extraction to meet local (not global) performance criteria (i.e., the goal is to limit pressure increases primarily where environmental impact is a concern). We evaluate the feasibility of IDPM for a hypothetical CO2 storage operation in an idealized multi-formation system containing a critically stressed fault zone. Using a newly developed analytical solution, we assess alternative fluid extraction schemes and test whether a predefined performance criterion can be achieved, in this case the maximum allowable pressure near the fault zone. Alternative strategies for well placement are evaluated, comparing near-injection arrays of extraction wells with near-impact arrays. Extraction options include active extraction wells and (passive) pressure relief wells, as well as combinations of both, with and without reinjection into the subsurface. Our results suggest that strategic well placement and optimization of extraction may allow for a significant reduction in the brine extraction volumes. Additional work is required in the future to test the general concept of IDPM for more complex and realistic CO2 storage scenarios.