Unfortunately, as Kiwi Flyer says above, the rules for stop-overs are program specific, from my own experience I know that SK are very stingy, especially on awards with other carriers (with their own awards they allow a stop-over prior to/after an intercontinental sector, basically a stop-over in CPH/ARN).

As for travelling to Baku (which I was loking into this spring but eventually went for Yerevan), the * Alliance carriers flying there are LH/OS/TK/BD and none of them have any service to the middle-east which would alllow a stop-over construction. For Baku however I would also look into BT (not * Alliance but partly SK owned so you can earn SK-points), they often have very good economy fares via RIX + they give out loads of points for little money in C.