There are some nuances about the levers of control that would be employed but generally, the President could one way or another stop the legal consequences in essentially any of these investigations.
For criminal charges, prosecuted through he normal chain of command at the Department of Justice: The president can order the Attorney General to stop the investigation and drop the charges, if any. If the attorney ordered to take the specific action won’t do it, they can be fired and replaced until the president finds someone who will do it. https://www.politico.com/news/2025/02/13/danielle-sassoon-eric-adams-prosecutor-00204146
If a special counsel is prosecuting the case, the answer is probably the same. There are special regulations in the Department of Justice that apply to special counsels to give them a certain amount of independence when pressing charges, but these don’t actually matter in practice. Smith special counsel investigation - Wikipedia
There are administrative agencies whose heads serve at the pleasure of the president, such as the Secretary of the Treasury. Again, the president can just order the Secretary to drop any investigation coupled with a threat of “do it or be fired.”
There are independent regulatory agencies, such as the Federal Trade Commission and the Securities and Exchange Commission, whose leadership is intended to be non-partisan. The SEC, by way of example, is led by a five member Commission. No more than three commissioners can be members of the same party. They serve for staggered five year terms, with one term ending each year. In theory, they can only be removed for cause, which is a limitation on the president’s authority to impose his will on the agency (see Humphrey’s Executor v. United States). But, the President appoints commissioners to serve and the president can choose any of the Commissioners to be the chair so if the current chair won’t do the president’s bidding, they can be replaced by any other commissioner on a moment’s notice. Over the long run, there is at least one chance every year to get a brand new chair of the Commission who will do whatever the president says. Worse yet, historically, when a chair is about to be demoted to regular commissioner (usually during a change of presidential administrations) the chair resigns from the commission, so the president then gets an extra seat to fill. It doesn’t take too long for the president to choose the chair of his heart’s desire. The chair also gets the power to direct the day-to-day activities of the staff, though there are certain powers that the commission can execute only by a vote of the whole body. So, if Musk were being charged by the SEC (and he is), the whole commission would have to vote to bring the charges or to settle or drop them. However, the chair acting alone can direct the amount of resources that the staff will direct to pursue the case, so a case could be killed simply by starving it of any resources. The current president has also taken steps to exert greater oversight of the rulemaking agenda of independent agencies. Trump claims expanded power over independent agencies : NPR
There are inspectors general at both executive and independent agencies that investigate waste fraud and abuse and legal malfeasance by the agencies. These IGs investigate allegations that, for corrupt reasons, the agency isn’t pursuing cases it should be pursuing, They are
supposed to benefit from some level of independence from the agencies they investigate but, it turns out, in this administration, they don’t. Trump uses mass firing to remove independent inspectors general at a series of agencies
The current Supreme Court majority is also hostile to the Humphrey’s Executor precedent cited above and seems to support a legal theory called the “unitary executive,” which basically means that the president ultimately has sole authority to determine how the laws will be enforced and to fire people at any agency he chooses (independent or otherwise), regardless of the limitations Congress has placed on the firing authority. If the court fully adopts this theory, and many legal commentators expect it will, the president wouldn’t even have to rely on lesser government officers to interfere with or drop investigations or prosecutions. The president could just do so unilaterally.
The president also has pardon authority.