Advantageous 4th outs can only come in the form of an appeal, specifically during relaxed action. By inference the ball is live, until the infielders have left the field, after the third out, but only relaxed action can occur. Any attempted advancement or retreat of a runner is ignored. The defense only need to touch home plate to complete the appeal, even if the runner is attempting to touch. This interpretation is an extention of the PBUC's ruling on a runner leaving the dugout to touch home.
EXAMPLE -- R3 misses the plate before the third out, and then attempts to retouch the plate after the 3rd out is made at another base. RULING -- R3's actions after the 3rd out are ignored, and the defense still may appeal R3's missing the plate by only a tag of the base. R3's run is contingent on a successful appeal.
Granted this isn't an official ruling, but I think this interpretation will allow the offense not to "screw" itself into trying to correct a mistake, but will still allow the defense to appeal.
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