I want to share what I've been trying so others can give it a whirl if they want to. I have been making whipped soap as a type of rebatch and it seems to work pretty well. I'm still working out the details, but here's the general outline --
Prepare a mold. If you grate 2 regular bars of soap, your mold should have a volume of 3 to 4 bars to contain all or most of the fluffier floating soap.
Grate bar soap into shreds. At the moment, I'm thinking the best type to use is a soap that has a firm waxy texture, not brittle and not soft.
Prepare any decorative additives, such as other shreds to add as confetti or whatever, and any fragrance or colorant.
Pour a cup or two of distilled water into a small pitcher.
Find a wide pot with lower sides -- a stainless steel or porcelain coated skillet or dutch oven will work well. A wide pan means there is a large heated surface on which to melt the soap. Lower sides make it easier for you to stir without getting too stiff or tired.
If you have a heat diffuser to "soften" the heat from your stove burner, use it.
Put the diffuser on the burner and the pot on top of that.
Turn the burner on medium low.
Put a small handful of shreds into the pot and let them start to melt.
Add tiny portions of water -- a teaspoon to a tablespoon -- as the soap begins to coat the bottom of the pan. Let the water evaporate before adding more. The idea is to keep the soap from sticking too much to the pan, but not to increase the water content of the soap too much.
If you see what looks like smoke rising from the pan, it probably is. Add a bit of water to cool things down, stir more frequently, and perhaps reduce your heat slightly.
Stir gently but often to keep the soap moving around the pan and melting slowly and evenly.
Add more handfuls of shreds and continue to melt until all the soap is in the pot. Don't add a lot of shreds at a time -- be patient.
Continue to heat and stir, adding tiny dribs and drabs of water as needed.
When the soap heats to 140 to 160 deg F (60 to 70 C), it will begin to magically foam and puff up like warm Marshmallow Fluff. Remove a small dollop and put it into water to see if it floats -- it should!
At this point, the soap shreds should be almost all melted. You can use a wire whisk or electric hand mixer to beat more air into the soap and also to smooth out the texture. Do this while the pan is still on the stove. A stick blender will probably not work because the mixture will be very sticky and somewhat stringy -- again, think Marshmallow Fluff.
When the soap reaches 150 to 160 deg F (65 to 70 C), mix in any additives, fragrance, and colorant.
Fill the mold. Pouring this sticky, puffy soap won't work well for me. I more or less threw spoonfuls of the soap into the mold to force the soap into all the corners.
If the soap sags in the middle as it cools, gently press the edges down so the top becomes flat again. I used a small flat piece of wood to press the edges down and it worked really well. The more water is in the molded soap, the more it will sag in the middle, much like a normal rebatch or HP soap.
Let the soap cool thoroughly before removing from the mold.
You may need to let the unmolded soap dry in the open air for awhile before cutting depending on the water content in the soap. More water = softer = wait longer to cut.
If you have a wire cutter, it may be possible to gently cut the bars and set them aside to dry further. If you must use a knife, you may need to wait longer.
And, yes, it still floats!