He and I sat down on the floor, and we dumped the entire toybox out on the floor. (Lunatic's parental recommendation? Put a tarp or something under the toybox if it's been a while. There's likely to be all sorts of crudulous junk in the bottom.)
I explained the rules: I knew that he had a lot of toys, and I knew that there were some toys that he never played with anymore, that he didn't like anymore, that were just no fun, and I knew that there was not enough room in the toybox for all of them anymore, and I knew he was having a lot of trouble finding the toys he wanted with all the stuff he didn't play with in there. So, he should sort the toys into three piles: one pile, in the toybox, of the toys he knew for sure he wanted to keep, the "Yes" pile; one pile, over there, for the stuff that he knew he did not want, for throwing out, giving away to someone who needed it more, or something like that, but definitely stuff that was going, the "No" pile; and a third pile, in the middle, the stuff he wasn't sure about, the "Maybe" pile. He could always take stuff from the "Maybe" pile and put it somewhere else later, but maybe he needed a little more time to think about it.
When the Little Fayoumis and his mom had sorted toys into Yes and No a while previous, there'd been a precious few "No" toys, and a lot of loud and intense wrangling. I was happy, but not entirely surprised, to see that the "No" pile was about 15%, the "Yes" pile was about 60%, and the "Maybe" pile took up the remaining 25%, versus the previous sorting of 90% "Yes" and 10% loudly disputed "No".
I had to rescue a few items that I know he played with a lot from the "No" and "Maybe", after it was all over, but it was accomplished without any yelling. He did go off task a fair deal, but a simple "Is that Yes, No, or Maybe?" got him right back to it.
We sorted the "No" pile into trash and charity/re-use, and I packed up the "Maybe" pile quietly out of sight, to go through later. (In practice, the "Maybe" items were generally "No"s in disguise.)
Active toybox volume was reduced by 40%. Mess on the floor was reduced. Dirt in the toybox was eliminated. Kid frustration at inability to find a specific desired toy was reduced by a few decibels. Success!