ASA Three-Man Question
 

Sitch: Bases loaded, less than two outs. Fly ball to medium right-center field. U1 goes out for the catch/no-catch. U3 goes to the area behind the circle to watch the tag-ups of R2 and R3. PU goes to the holding zone near the third-base line and watches R1's tag-up.

R1 tags and attempts to score. F8's throw comes toward home, so U1 starts to shade back to the plate for the play. The ball is just short of home, so F2 steps up, catches the throw, and makes an immediate throw to third to play on R2, who tagged and is advancing. R3 also tags and is heading to second.

By the Manual, if I understand it correctly, the play at third belongs to the PU. But he positioned himself for the play at the plate. Should U3 take the play at third? And should the PU inform U3, "I'm going home!" or something similar to let U3 know he/she should take the play at third?

that would not be correct under this situation. The throw from F8 was towards home plate and was subsequently 'cut off' by F2. The next throw to third base would be U3s call (as we are now in a 2 man system) this is one of the 'four' exceptions where a base umpire will make a call at a runner at third base on a ball hit to the outfield.

This is BU's call (and U3 became BU when U1 went out). PU doesn't need to call out anything, as BU knows 3rd base is his call once the throw goes home.

Ugh, you are correct. I went straight to the Three-Umpire System in the book before reading up on the Plate Mechanics section. Thanks for the heads up.