Just today I rang the Flight Centre, re upgrading to Business Class with Singapore Airlines, using Air New Zealand air points. Like UA, Singapore Airlines is a member of Star Alliance.

To cut a long story short we could not upgrade from tourist to business class, on Singapore Airlines, but we could purchase a business class seat and use the Air New Zealand points for the other seat. The catch is, it would cost 25% more in air points. I don't know if this helps.

Regards, Richard Bloomfield(New Zealand)