The Military Police are a division of the Crimson Blade, a part of the Gudersnipe Foundation. They are responsible for providing police services anywhere the Foundation has a strong presence. MPs also operate aboard Foundation starships, providing security as well as handling criminal actions among the crew.
The Military Police are backed by the Foundation, and as such have effectively unlimited resources. They also utilize military-grade equipment and operate the same vehicles as Crimson Blade soldiers. With the Foundation being eager to label practically anything a "training excercise", MPs have little difficulty getting their hands on massive amounts of manpower.
While resource mismanagement is always a concern, MPs are effectively never told the department "can't afford" something. Rather, the question is whether or not the use of resources can be justified.
Foundation Military Police have multi-national jurisdiction and can cross nearly any border in pursuit of a suspect. The agreement was made a part of every Foundation treaty in the early Second Age and only treaties that predate it have the possibility for a provision forbiding MP jurisdiction.