Originally Posted by
soitgoes
If you earn using the SPG Amex, you can transfer points to AA miles and not only get around that cap, but get a 25% bonus on transfers in 20K blocks.
Come to think of it, the same way of getting around the annual cap (but with no bonus, except for occasional promos) should work with Diners Club too. DC, thanks to their deal with MasterCard, is accepted in many places that AmEx-branded cards aren't.
(And thanks to
Boraxo for a very clear explanation of that other bit.)