Linear regression on an usual domain, hyperplane, sphere or simplex

I was wondering if you are aware of any methodology to perform multivariate linear regression on non-standard spaces or domains. I try to reverse-engineer the recipe for the coca cola beverage. The response, Y, is how close my recipe is to the actual formula, based on a number of tastings performed by a number of different people, according to a design of experiment plan. Indeed, it's quite similar to a clinical trial where a mix of atoms or chemical radicals (each combination producing a unique molecule) is tested to optimize a drug. The independent variables are binary, each one representing an ingredient: salt, water, corn syrup etc.