There's plenty of "flavors" that it's hard to say are specifically coded for with dedicated receptors,
I'm not sure if you're aware, but taste and flavor are not the same thing in the culinary world, and I assume the scientific as well. Taste is strictly what comes from the taste-buds on the tongue. (Saltly, sweet, sour and bitter; with other tastes being debated.) Flavor, on the other hand, is the combination of taste, smell, mouth feel, temperature, appearance, etc. That's why there's such an argument over what is taste and what isn't. It's easy to isolate the four major tastes, because they're triggered strongly, and to the exclusion of other tastes, by common compounds. Salt, sugar, acids and I'm not sure what the simplest bitter compound is.
It's previously been assumed that umami was just a type of salty, and some still argue that point. Other candidates, like metallic and carbon dioxide, are assumed to be part of mouth feel, a touch sensation rather than a taste. The article explains why there's reason to suspect that those have specific chemical receptors on the tongue that would classify them as taste rather than touch.
