Contrary to what many out there believe, soap does not make more room in water or mops! The only thing soap does is lift dirt and oil into water, making them suspend (aka float) in the water by using the power of something called surfactants. Surfactants have a hydrophilic (water-loving) tail and a hydrophobic (water-hating) head and look like chemical sperm, no really! The head sticks to the oil and dirt and the tail pulls it up into the water. The longer dirt sits in soapy water the more covered it becomes with little surfactants, till it is coated on all sides. This is why when you pour dirty rinse water into a sink, the dirt does not stick to the sink and slides down the drain instead.
The water you use when mopping, whether it be on the floor, in your mop pad, or in your mop bucket will eventually get saturated with dirt. Adding to the problem, the mop pad you use when mopping will eventually get saturated with soapy water as well, often well before the water is saturated with dirt. At either of these fail points no extra amount of soap will be able to lift dirt into water or force more water into the mop pad, meaning you will just be smearing dirty water around. What this also means is that if you don't properly absorb all the soapy water on the floor, you aren't removing all of the dirt and soap residue and it may then form streaks on your floor (if you have laminate floors check out this guide on how to safely deep clean laminate floors without streaks)