If you goal is to use miles for free flights, American Express (including the more effective Starwood card for transferring points to some carriers) allows miles to be transferred to some *G carriers (not UA), which can then be used to redeem for award flights from that carrier as a code share on UA, often with arbitrage in your favor (costing you less total miles for the same ticket that would otherwise have been bought on UA with M+ miles, especially with SPG miles to ANA). Obvious restrictions on capacity exist but as your Amex points are transferrable to 17 carriers, you may have even more flexibility than just earning M+ miles. The miles may be less useful on other *G carriers if you want to use them for upgrades...

The online zine First Class Flyer often discusses this strategy...