This would be an issue of national security. I would not want to be the person who spends money to set up drilling toward the Yellowstone Supervolcano without alerting the US Department of the Interior of the plans.
I can only imagine that such a massive enterprise would be entirely conducted by the US Government, probably any of the military branches(is Engineers Corps still a thing?)
The Army Corps of Engineers is a thing... their civil works authority makes them the final authority on water management (changing river flow, dams, anything related to water management.) Not sure about supervolcanos though, couldn't find that on their website.
I am sure that a minimum of the US Geological Survey and ACE will be involved in any supervolcano remediation plan. And probably FEMA but hopefully they won't need to act. ;)