Under the separation of powers in the constitution, theoretically, the president can authorize departments in his branch of government to be sponsored by a private corporation to gain funding outside Congress. This policy is a slippery slope where the private corporate sponsor can exert an anticompetitive market power advantage and refuse to work or sell to its competition.
Here is an example.
The American satire "Idiocracy"Corporal Joe Bauers discovers in the future our nation's crops are irrigated with a sports drink named "Brawndo" whose parent corp. had purchased the Food and Drug Administration, Federal Communications Commission, and United States Department of Agriculture. Our President needs to create a policy where this never becomes reality.