Ever have a project sponsor hand-pick a steering team that they know will support all their decisions, even if it's not the best solution for the enterprise? To avoid this, consider a "grand jury" approach, where a select group of managers "serve time" on a common steering team to address whatever critical projects come up during that time (let's say 6 months), with the goal of making enterprise decisions for each project that comes their way.
Like a real grand jury, this team wouldn't sit every day; they'd meet at a set interval (either weekly or less frequently as needed). This would be different than a traditional governance council in that this team would operate more at a tactical level as opposed to project and stage gate approval. Just something to think about.