I've done the, send the 3rd pilot ahead and it seems to work out best. But:
It's not condoned by FSI or ISBAO, or anyone else for that matter.
It's costs more money, an airline ticket, a hotel, a day off, a meal or two. Yada Yada
Most tech stops are in so so spots, ANC or Helsinki or Russia, you get the idea. You also run the risk that you may not actual stop at the airport where the relief pilot is. Then what?
Even with all that I still like the one fresh guy Vs 3 tired guys approach. It's always helpful to have a friendly face at a strange FBO making sure that things flow smoothly.
When we take 3 in the aircraft we wait until level off, look at the time until top of descent and then subtract 30 minutes (10 minutes for each guy to freshen up and swap out). The remaining time is then divided by 3, that's your rack time. The jump seat guy takes the first break, then the other two guys either play coin of fate or the United Nations approved treaty negotiations tool (rock, paper, scissors).