Apparently in the Clinton trial witnesses were called after it was voted on because the Senate can define the process:
In a Jan. 11, 1999, interview on CNN's "Larry King Live," Biden suggested he was "open to the prospect of witnesses" but only if House Republicans who were managing Clinton's impeachment in the Senate "make a case as to why they didn't see any need for any witnesses and now they think they should call witnesses."
Yet Biden and other Clinton allies — including now-Senate Minority Leader Chuck Schumer (D-N.Y.) — lost the witness fight during that 1999 trial. The Senate agreed to depose former White House intern Monica Lewinsky, whose affair with Clinton led to just the second presidential impeachment in history, as well as two other witnesses.
https://www.politico.com/news/2020/0...witness-109730