Recently, I've been experimenting with adding synthetic surfactants to liquid soap, and I like the results. My goal is to produce a more mild product through the use of less coconut oil, and through the mixing of surfactants with different ionic natures.
Using less coconut is easy--just use less. As was noted in a previous post, a squirt of liquid soap tends to apply more soap to the skin than a bar, and as a result, the product can seem more cleansing (than a bar with the same FA profile). Reducing the coconut will help, but it also decreases the lather. Additionally, I find that LS is less quick to lather than a bar, and the thicker the soap, the harder it is to work it into a lather (at least, in my experience). The sum of all that, is that a product with less coconut may clean, but is not easy to use (and provides few of the sensorial aspects that I have come to expect). That is, unless you use a thin soap and a foamer bottle (my preference for hand washing!), or introduce some synthetic surfactants.
In spite of the scare-mongering around the internet, surfactants don't have to be scary, and I'm pleased to hear that you have some on hand and are willing to try it in liquid soap; a small amount of surfactant may go along way towards making your end product more mild and more easy to lather.
Generally speaking, mixing surfactants of different ionic natures (cationic, anionic, non-ionic, amphoteric) is a good thing as it produces a milder product. Recently, I've been mixing liquid soap (anionic) with coco glucoside (non-ionic), and my observation is that the resulting product is more mild on my hands (I have not tried it in the shower yet; maybe today), it lathers quicker and is thicker. I was able to manage all of this with just 6% coco glucoside (and 24% soap, 10% added glycerin, 60% water). I'd also like to note that the only LS I have on hand right now is formulated with 29% coconut. It's more than what you want to use, but it's important to note that even with that high amount, the product is more mild with the addition of a non-ionic surfactant.
This net result of a milder product ( I believe) only works with mixing different ionic strengths of surfactants. I assume that your coco betain is cocamidopropyl betaine; if so, it is an amphoteric surfactant and as a result of the pH of soap, will be negatively charged when mixed with liquid soap. I don't know enough of the chemistry to know if that makes it "anionic," but my thought process is that it won't be as mild when mixed with soap as it would be if mixed into an acidic solution.
With all that said, I say give it a try! Start small and if you don't get the results you're looking for, look at a different surfactant; I'd recommend something non-ionic. Unless you have one on hand, I'd stay away from the cationics; I once tried using a cationic conditioning ingredient (polyquat 10) in liquid soap and while it left a great skin feel and thickened the soap better than anything else I've tried, it STUNK, and eventually produced some sort of light sediment. Sediment I can live with--but not stink.
