The presidency has been enhanced beyond its expressed constitutional powers.
An official representative of one country to another, empowered to negotiate and represent their country but often stationed inside the foreign capital
Top-level department heads that advise the president
Commander in chief
The president's role as the top military official
Agreement made between the top executives of two governments, without the force of congressionally-ratified treaties and revocable by future presidents
The relationships between the United States and other nations; often conducted by the president and executive branch
When the House through a majority vote accuses an official of treason, bribery, or high crimes and misdemeanors
The Senate conducts this proceeding, and if they vote to convict with a 2/3 supermajority the official is removed from office.
When the president names someone to sit as either a federal judge or a Supreme Court justice.
Not signing a bill for 10 days, but Congress isn't in session at the end of the 10 days and the bill dies.
What a president does with a bill that s/he doesn't like but signs into law anyway, indicating disagreement because a veto would likely be overridden
When the Senate by a 2/3 vote approves a treaty signed by the president.
The president's ability to say no to a bill. Sends it back to Congress, where it dies if not approved again by 2/3 in both chambers.
When both the House and Senate vote to pass a bill that has been vetoed by 2/3 majorities, the bill becomes law over the president's objections.
White House staff
People that work inside the actual White House office space, but not for a particular cabinet department.