Very easily:
Let's say HB1234 "The Waste Taxpayer Money Act" has passed the House and is awaiting action in the Senate.
The Senate can take HB1234 - amend it by gutting it completely and renaming it - pass it, and send it back to the House for consideration and a vote.
This happens pretty often - is legal - and gets around the "All spending bills must originate in the House" issue.
This happens at the state level also.