As I've mentioned elsewhere, I've had better luck geting upgraded to suites overseas.

Most recent: November-December, upgraded to suite, Munich Mariott Renaissance

January - Upgraded to suite, Marriott Grosvenor Square*

Not all Marriott stays get the upgrade to suite, but at least some do.

*(Since the January trip to London, I've mainly been in Starwood properties, so have no more recent experience.)