The short answer is "It depends". The longer one is the following: Aleppo soap requires sodium hydroxide to be mixed with oil and water in order to yield a hard soap. This chemical reaction inevitably yields a solid product. To produce a liquid soap, one substitutes sodium hydroxide for potassium hydroxide. What is desired with this substitution is a reaction that doesn’t reach its full potential, meaning that it stops before the final product (a hard soap in this case) is reached. With potassium hydroxide, the chemical reaction is incomplete, consequently, some hydroxide will remain in suspension in the soap. The production process has achieved what the consumer wants; a liquid soap, but at a great cost. Let me explain. The presence of unreacted hydroxide compounds opens up a Pandora box. First, the remaining potassium hydroxide is corrosive to the skin thus forcing chemists to add glycerine and synthetics to counter its effect. Second, potassium that has not reacted will settle at the bottom of the fluid and thus some emulsions will be needed to stabilize the mix.
In short, a natural liquid soap is hardly achievable with today’s knowledge, or at least let’s not call it a soap because it contains impurities and additives.