You can with an Amex issued card.When the CBA asked me if i wanted their amex as well I specifically asked about SPG and they said no-just what their visa,MC cards can transfer to.So really just check what your bank offers.
I would think the double transfer to SPG isn't that great but I always transfer the other way.
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The only 2 cards I'n aware of that TF to SPG are Diners and Amex issued Amex cards. They both TF at 2:1 ratio. ie 2 reward pts: 1 spg.