How to get upgrade from Y to PE?

[cgichard]

I have a confirmed MEL-LHR return booking paid in full for May & July next year. On my preferred flights I was able to secure only one segment in PE; for the others I picked Flexi Y fares as they are supposed to be upgradeable. But when I clicked on the Upgrade box on the Manage My Booking, the message was that I couldn't upgrade on those fares. Is there a way to position myself for an upgrade to PE for any of the 3 segments booked as Flexi Y?