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?
Not true. There are 18 witnesses cited in these articles of impeachment. Calling them for testimony in the Senate phase is the up to the Senate. This isn't a Perry Mason episode.