Are you talking about making the initial paste with water and then diluting with glycerin? If so, I think I may have heard of some people on another forum doing that, if I remember rightly (this was a few years ago, so I could be remembering it wrong). Anyway, I myself actually do the opposite: I use all vegetable glycerin to make the initial paste, but when I dilute it, I use distilled water.
Benefits of thickness. I can't find the article now, of course. I use distilled water at the dilution and it worked fine. But I read either full glycerin or half and half for dilution. I may try it and give it a go. Who doesn't always need more soap!
One tip is to not take the dilution rate in a recipe as gospel truth. Sneak up on the dilution a little at a time and you'll stand a better chance of getting the thickness you want. It's easy to get impatient and overshoot.
Another is to use a high % of oleic acid in your LS recipes. You'll see a wider range of water concentration where the LS is a nice consistency. It is the nature of oleic acid to be thick over a wider range of water %.
Well thickness. Strange thing is when you read a body wash from the store it sometimes has both koh and Naoh. The soap I just had was supppppper thick. So it seems I may just be doing this from now on. I actually used 1 part naoh to 2 parts koh.
Depending on your formula, you can get liquid soap that's as thick as honey, or even sweetened condensed milk, I daresay- with using only KOH. My cocoa-shea GLS formula with KOH-only is super-thick with the consistency of sweetened condensed milk poured straight from the can. As a matter of fact, if it were any thicker, I am quite certain it would not dispense out of my pump dispenser. lol