Ashton Agar and Usman Khawaja are the other two names doing the rounds, as the visitors grapple with injury issues ahead of the third Test here starting Thursday.
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The four-match Border-Gavaskar series is poised at 1-1.
While Maxwell has the advantage of being part of the touring squad for the entire trip so far, Stoinis can stake a claim as replacement for Marsh given his all-round skills and strong seam bowling.
Maxwell was not even in the Victorian Shield side at the start of the summer, having been dropped seemingly as a result of his unsuccessful attempt to move north to New South Wales during pre-season.
Stoinis has been the Bushrangers' preferred choice at No. 3 for several seasons and has done so with success - until this season.
First Published: March 13, 2017, 7:14 PM IST