Is there a way the US president could extend his immunity in the future?

Question

"However, the Court ruled in Clinton v. Jones, 520 U.S. 681, 117 S.Ct. 1636, 137 L.Ed.2d 945 (1997), that a sitting president does not have presidential immunity from suit over conduct unrelated to his official duties. The holding came in a civil suit brought by Paula Corbin Jones against President Clinton." (U.S President legal definition of U.S President)

Is there a way a sitting president could extend his immunity in the future? For example, to also cover his activities as owner of private companies?

Answer 1

No. That presidential immunity is strictly to prevent a president from being bogged down and unable to perform his duties, so they put oversight of actions taken in the course of being president in the hands of Congress, who can act via impeachment and trial if actions as the president warrant.

Since this partial immunity is born of necessity and function, not as some sort of imperial perk, there would be no reason to have it extended, and any president trying to get those kinds of powers would be flying strongly against democratic principles that are supposed to be the foundation of the US system.

In Fitzgerald vs Nixon the court found that the immunity granted was very narrow -

"we need not address directly the immunity question as it would arise if Congress had expressly had created a damages action against the President of the United States.... Consequently, our holding today need only be that the President is absolutely immune from civil damages liability for his official acts in the absence of explicit affirmative action of Congress."

To further illustrate the functional nature of the separation of official and non-official actions, the Congress can't impeach, try and remove a president for actions not taken as the president, since "High Crimes and Misdemeanors" are specific to official conduct -

I have carefully researched the origin of the phrase "high crimes and misdemeanors" and its meaning to the Framers, and found the key to understanding it is in the word "high." It does not mean "more serious." It refers to those punishable offense that only apply to high persons, that is, to public officials, those who, because of their official status, are under special obligations that ordinary persons are not under, and which could not be meaningfully applied or justly punished if committed by ordinary persons.

Meaning of "High Crimes and Misdemeanors" by Jon Roland, Constitution Society

So, to sum up, actions not taken as part of actions performed while president or, especially, as part of being the president are not protected, and Congress has oversight of presidential actions, but only presidential actions.