UPDATE: Seems as though this is not possible and API keys are tied to one specific org.
I read that this is possible using Basic Auth like this:
And I have tried the same endpoint with an API key and I get a 404.
Background Info: I need to pull panels from specific dashboards associated with specific orgs. However, I am only able to do this when a dashboard is associated with the current org. Therefore, I need to switch the current org to the org that has the pertinent dashboard before I query the API for a panel.