A "stiff drink" is just a strong drink, one with more alcohol than mixers. So stiffen would mean put more alcohol in it. I sometimes call that "Irishing it up".
I've never heard "soften" used in the context of alcoholic drinks. To me, "soft drink" only means "soda".
I'm not an expert. My drinking is fairly low-brow. When I drink, I drink to get drunk, and I tend to drink random spirits mixed with random fruit juice; there's little art to it :D
This post was edited by Benedict Arnold at June 1, 2017 12:33 PM MDT
To stiffen aa drink is to add more alcohol. I've never heard of softening a drink, but softening water (by filtration or adding chemical reagents) is done some places where the water has a high mineral content - called "hard water". Soap won't lather and it plays hell with your plumbing, so the water is "softened".
Benedict Arnold 