Thank you for your reply.
I was looking at the SQ website, and noticed that the cheapest, non-upgradeable fare was 1200€ return (BRU-FRA-SIN-AKL). The full flexi fare was 1800€ (which I guess is still cheaper than a discounted business ticket) and it was specifically mentioned as "upgradeable with Krisflyer miles".
Are Krisflyer miles the same as M&M miles, or am I out of luck?
Sorry for being such a noob