Do you think a 4th branch of the federal government, dedicated to continuously investigating the other three?

I'd call it the "Investigatory Branch", and it would subject every elected and appointed member of the executive, legislative, and judicial branches to constant investigation on everything they do in their public and certain aspects of their personal lives. We clearly need this, whether you believe all the made up Obama and Clinton scandals, or the very real Bush and Trump scandals.

It would be set up to give the other branches as little influence as possible. The nominees would be selected from a national pool of sworn apolitical and nonpartisan law enforcement professionals, vetted by INTERPOL. The members would be banned from having any membership or involvement with political parties beyond voting in primaries and elections. They would not be political appointees, but be career civil servants.

If the Investigatory Branch found wrongdoing, they'd be required to publish their findings within 96 hours, and to issue recommendations to either congress or the Supreme Court on whether the official being investigated should be removed from office or charged with a crime. They would also have the authority to remove criminals from the higher levels government.

This branch would have no operational secrecy, and be required to publish every internal document without redaction within a year. In other words, everyone else would watch the watchers.