So, instead of a cat cave, I used up all the bits of bulky yarn leftover from previous projects. Mostly all those fox and wolf hoods I made the winter before for Christmas gifts for the kids. It worked up fast, I didn't have to buy new yarn, and if he was uninterested I could donate it to the local cat shelter. He liked it.
He really liked it. He went a few weeks without using it here and there but he kept going back to it, so it remained.
One day I was looking at that flat circle and decided it needed structured walls. I had made an ever expanding circle for the base and worked without increases for the walls, standard fare for making crocheted bowls, etc. But the walls just flopped down and laid there.
I had some leftover foam from making camera bag inserts so trimmed that to fit the height of the wall. I created a V by starting where the base and wall bet and crocheting either 4 or 5 rows around, whatever it took to reach the top with a little leeway. I inserted the foam in the pocket created and slipped stitched around to close up the pocket. I left a small opening in front. The opening is pretty standard but also happened to be the result of how much foam I had to use.
And Mr. Max is happy. He loves his cat bed with firm, structured walls even more than he liked it with floppy walls.