President Trump recently made a statement about suing Pelosi and Schiff over the impeachment inquiry.
Can the US President sue political rivals?
What would he sue about? How would that work in practice?
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In theory a president can still do things in his capacity as a private citizen, such as going to see a movie, singing and dancing in the street, or even suing someone.
In practice (for previous presidents, at least), the office itself is so busy that presidents rarely have time to do much outside of their job. And the office carries so much symbolism that one's words end up carrying the weight of governmental authority, no matter how much you might try to disclaim it.
This is why previous presidents avoided acts even as innocuous as wearing a t-shirt with a logo on it; this could be interpreted as implicit endorsement of the logo. It looks bad for the presidency, it looks bad for the president. Better to dodge that whole mess. Getting entangled into a private legal dispute would look even worse.
But these are all guiding principles; they are not strict rules. And if there is anything Donald Trump is known for, it is openly disdaining, disregarding, or just being plain clueless about, any kind of established principles. He also doesn't care much about looking bad either; he has such a scummy reputation that one more lawsuit could not really make things look worse.
That said, Donald Trump has a long history of talking big and chickening out. Especially with regard to lawsuits. He's happy to sue little defenseless people who cannot fight back. But someone with resources like Joe Biden? He doesn't have the courage.
Trump said "sue him [Schiff] anyway, even if we lose, the American public will understand". That should tell you the gist of this. No specifics were given by Trump's lawyers:
Trump's attorney Jay Sekulow told CNN the President's legal team is "looking at all options" after Trump floated the possibility of a lawsuit against Schiff and Pelosi. "Nothing off the table," Sekulow wrote in a text to CNN. He wrote they are "in the research stages," suggesting no legal action is imminent. "The pattern and practice of irregularities in this inquiry is reminiscent of the irregularities in the Mueller investigation," Sekulow said. "No President should be subjected to this political theater."