** Shares of Brazilian Rare Earths BRE.AX extend gains to rise as much as 24.4% to A$2.4, their highest since January 22

** Stock last up 20.2% at A$1.93, set for strongest session ever

** The rare earths miner on Monday amended acquisition terms with Rio Tinto Brazil to replace milestone payment with production-based royalty payment for the Amargosa Bauxite project in Brazil

** About 262,613 shares change hands, 1.1x the 30-day average of 232,298

** Stock down 1.7% YTD, including moves in current session

(Reporting by Jasmeen Ara Shaikh in Bengaluru)

((JasmeenAraIslam.Shaikh@thomsonreuters.com;))