(Recasts; updates share movement, adds analyst comment)
** Shares in Caltex Australia fall as much as 4% to A$31.38, bigger than the broader market’s near 2% drop
** To engage with suitor EG Group for a better offer after calling the A$3.9 bln ($2.54 bln) offer for its convenience store business and plans to list the rest too low
** Also has a twice-improved A$8.8 bln offer from Canada’s Alimentation Couche-Tard Inc for all of Caltex
** Shares at lowest level since November 2019, and posts biggest intraday loss since August
** Couche-Tard remains in the box seat despite Caltex willing to engage with EG, and reduces likelihood for a higher Couche bid, if EG or anyone else does not come in with a higher one - RBC Capital Markets
$1 = 1.5344 Australian dollars Reporting by Nikhil Kurian Nainan and Aditya Munjuluru
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