OS X Mountain Lion 10.9.5 upgrade
I have the same question that Graham asked in 2018, but the Apple iMac support answer doesn't address the issue properly or solve the problem. When I follow the Apple Support instructions and click on software upgrade from the Apple drop Down Menu, the system states that there are "no compatible upgrades available." It also shows 2 incompatible updates for iMovieversion 10.1.14 dated 12/10/2019, and iPhoto version 9.6.1 dated 3/19/2015. My iMac is a model 13,1 from late 2012. The Apple Support Tutorial shows that this System should be upgradable.
iMac Line (2012 and Later)