"...What would one use to increase the PH, just increase the amount of LYE to the initial solution and limiting your superfat?..."
If by "increase the initial amount of lye to the initial solution" means to use a more concentrated lye solution (say 40% NaOH rather than 28%), all that does is increase the rate of saponification. Limiting superfat doesn't work either. I've made soaps with as much as 40% too much lye. While these soaps were certainly high pH soaps for awhile, they were zap free soap after a couple of months. It's the nature of soap to reach a pH that is natural for it and stay there.
What is the harm of having excess lye in a hand soap? Sensitive, itchy, burning sensation. Redness, roughness, cracking. Eventually dermatitis or possibly chemical burns.
When I'm not playing mad scientist and instead am making soap for regular use in my home, I want to make a nicely formulated soap that has a pH normal for that particular blend of fats. If it's a laundry soap, I limit the superfat to prevent any excess fats in the finished soap (NOT to adjust the pH!) and I use a lot of coconut oil for fast dissolving and strong cleansing ability. If it's a bath soap, I formulate a soap that lathers well, is mild and safe for the skin, lasts a reasonably long time, and looks and smells nice.
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For the record, adding citric acid does NOT lower pH UNLESS there is excess lye present. If there is no excess lye present, then the soap breaks down into fatty acids, releasing OH- ions to react with the H+ ions released by the acid. The pH remains stable as long as this fatty acid breakdown is going on. Keeping the pH stable despite the addition of acid or base is normal behavior for what's called a "buffered" system. That's what soap is -- it acts as a buffer.
Up to a point, this breakdown in a bar soap from soap to fatty acid is not perceptible to the user, but it's there. If enough acid is added, a bar soap will become soft, mushy, and greasy feeling. In a liquid soap, the breakdown is unmistakable -- there will be a layer of fatty acid floating on top of the soap.