I can definitely do that Sharps! The one thing to remember about soaps and their ingredients is that the base is (IMHO) about 60-70% of how the soap performs, the rest is how it's processed and saponified. You can have two soaps that have the exact same ingredient list, to the mg, but are produced differently, (cold process vs. hot process, ingredients added at different points, etc...), return very different performance properties.
Point in case, Noble Otter has a relatively short ingredient list but performs almost as well as something with 3-4x the amount of ingredients such as WK Donkey Milk formula or B&M's reserve base. It can be counter-intuitive at times. Martin de Candre only has 7 ingredients and is a phenomenally good soap.
I haven't done much of any research into individual ingredients, (the different butters and oils and their benefits to shave qualities), something I'll have to do prior to doing a video on this subject. CBLindsay would be a good person to ask as he's done a LOT of trial and error and research into soap ingredients.