Once again, you are confusing trials with the function assigned to the Senate in consideration of an article of impeachment. They can ONLY consider the evidence presented to them by the House and the arguments provided to them by the defense. Period. The House says "He's guilty of this, this, this, and this. The Senate then judges their case of this, this, this, and this. There is no constitutional basis to then allow the House to then say, Oh, by the way, he might be guilty of that too. If they want the Senate to Judge "that", then the House needs to gather "that" and present "that" for the Senate to judge.
Think of it this way. The House cannot force the Senate to judge an accusation that is not presented as an article of impeachment. By asking for "new" evidence/testimony, this is actually what they are attempting to do because this "new" evidence/testimony is not part or parcel to the articles of impeachment currently being presented to the Senate.
The manner in which they present this to the Senate is with an article of impeachment. The constitution gives the power to formulate an article of impeachment SOLELY to the House. The Senate is disallowed from developing their evidence and allowing "new" testimony is exactly that.
I don't think anyone's asking to bring new charges.
The House cannot force the Senate to judge an accusation that is not presented as an article of impeachment. By asking for "new" evidence/testimony, this is actually what they are attempting to do because this "new" evidence/testimony is not part or parcel to the articles of impeachment currently being presented to the Senate.
New evidence is not a new accusation, it adds additional weight to an existing one.
You do realize that there's no evidence in the articles of impeachment, only accusations. Right?