Soap is synthetical, correct. In my bathroom that container, round lid, the transparent soft material, in Muji water and the used smaller soap, 1 or 2 right now still in there.

You say they multiply because on the back of your toilet sink, you can dump some of that water in it. Its the soap. But they were in the solid structure being dissolve, so every time you re-fill that container with the water, the soap will be "soaked" in the format, that water its the soap water.

You feel it multiply, because the soap are being dissolve in the water.

Its those your small soap you cannot use by your hands dump in them.