Well, all prices are still determined by the intersection of supply and demand.
I'm not saying that the objective features are IRRELEVANT to a consumer's purchase decision, obviously they're not, but ultimately each person values what they're buying differently than the next person.
I'll run with your coffee example:
Let's say someone currently values a cup of Starbucks at $6 / cup and Starbucks is selling it for $4 / cup. If Starbucks raises their prices above $6 / cup (to $20 like you say), that person would no longer purchase Starbucks coffee unless their values change. But there's a good chance that SOME people (a small minority no doubt, but probably not zero people) currently value Starbucks at more than $20 / cup, those people would continue to buy coffee from Starbucks unless their values change.
As prices for Starbucks coffee increase and exceed the amount that individuals value it, those people will begin to explore alternatives on the market to determine if there is another comparable good that meets their needs at a price less than they value it.