"maximum leverage" means using the most advantage or power you have to get what you want or achieve your goals. It refers to using everything at your disposal to make the biggest impact or achieve the greatest result possible. Full definition
Advocates had hoped for some action in the budget process, considering that the governor tends to hold maximum leverage in the negotiations. (nystateofpolitics.com)
That reform - for - pay trade was thought to be the governor's maximum leverage at the time. (nystateofpolitics.com)
The key to getting consistent reviews with maximum leverage is to put a system into place so it becomes second nature. (realtormag.realtor.org)