Any ingredient that contributes to speeding up the chemical reaction, also increases the heat and contributes to volcano formation. Also the size and shape and what the mold or vessel is made of can foster or support that heat and volcano formation by containing the heat in the center. Higher heat to start will also contribute. Higher Coconut Oil content will contribute to faster heat production. Also higher ambient temperature of the area where the soap is being made or left to sit and saponify will contribute. Processes, such as over-stick-blending can contribute to overheating. Once the heating up is accelerated, it continues and will not stop until it runs its course unless interrupted. Sometimes that leads to volcanoes when the inner core gets so hot that the heat has to escape.
Ingredients that contribute:
sugar-containing ingredients, such as table sugar, milks, juices, carbohydrates (oats, etc.), fruits, etc.
alcohol-containing ingredients, such as beer, wine, kombucha, OJ, fermented drinks, etc.
high water content in the lye solution supports higher heat production during saponification
Coconut oil heats up fast in the presence of lye - IME this can happen quickly with higher percentages of CO in the formula.
Some fragrances, such as some spicy and some florals tend to speed up the heating process (accelerate)
Vessels that contribute:
anything that holds heat in or insulates, such as wooden molds
coverings, such as lids on top of molds to hold the heat inside
shapes that keep the majority of the soap very compact and close together, especially with a large volume of soap
Opposite - if you want to discourage overheating:
Use less water in your overall formula.
Soap at cooler temperatures when able, or at least as cool as your ingredients allow.
Use fewer or decreased amounts of ingredients that contribute to overheating or cool them first and mix them in very slowly using a whisk & vessel that allows more heat to escape from the surface and possibly use a cool-water bath during the process.
Use molds that give the soap more surface area exposed to the air so the heat cannot build up in the center, such as slab molds or small individual molds.
Avoid insulating the molds for formulas that tend to overheat and raise them up off a flat surface, to allow additional air-flow on the bottom portion of the mold. (This can stop a volcano that starts in its tracks.)
Some folks refrigerate the molded raw soap, but that is no guarantee as I have seen photos of soap that volcanoed and spilled out of the mold onto the inside of a freezer!
I have placed molded soap on cold concrete to bring the temperature down quickly, and that can help prevent overheating, as would putting the soap mold on a tray and the tray atop a cold surface, such as ice packs or above a bowl of ice.
I may have left out some things, but that's pretty much all I can think of at the moment.