Oh, I must take my Expedia criticism back. It is outdated.

It turns out that you can select any Finnair ticket family. "Upgrades" include Basic (i.e. Light+bag), Value, Pro and Business. I guess Amadeus and Expedia have been busy. In the website, they are listed below the itinerary after all flights are selected. In the Android app, there is a button at the equivalent stage. This is with Expedia France - did not try with other country sites.

I don't know how well it works for complex itineraries though.