How do I reduce the smell of store-bought liquid soap? I recently bought a brand of liquid soap I've never used before and it turns out they formulated it with a bit too much of the scent ingredients, to the point where I find it gets uncomfortably close to nauseating during use, and also it persists too long on my hands afterwards, compared to what I find normal.

How do I neutralize some of this scent, what can I try to mix in? All I can think of are baking soda or vinegar (but then vinegar also persists a lot and is unpleasant, plus it's acidic and I'm going to mix it with a probably-alkaline soap, and I don't want any crazy reactions and byproducts if possible).
If the scent reaches out and touches you that much, it is likely volatile. Pour it in a pot, add a volume of water, heat on a hot plate outside your dwelling till the smell goes away. Evaporate to volume and check ingredients. You may want to add back a small amount of a desirable ingredient that boiled off. Raise the temperature slowly. A vigorous boil will make a real mess.