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With two outs, you have to find a ruling you like. I tend to enforce the same ruling when there are NO outs, one out or two outs.

Case: 2 outs, R3, R2, ground ball to OF fired home. R3 scores easily and R2 is thrown out at the plate. The B/R returns to the plate to pick up the bat and instruct R2 to slide. The pitcher sees the B/R's action and tells the catcher to fire the ball to 1B for an out. Does it count as an advantageous 4th out and take away the run scored by R3? I say it does and if you don't want to agree with SAump, fine.

Would your ruling change with 1 out?

Case: 1 out, R3, R2, ground ball to OF fired home. R3 scores easily and R2 is thrown out at the plate. The B/R returns to the plate to pick up the bat and instruct R2 to slide. The pitcher sees the B/R's action and tells the catcher to fire the ball to 1B for an out. Does it count as the 3rd out and take away the run scored by R3? I say it does and if you don't want to agree with SAump, fine.

Would your ruling change with 0 out?

Case: 0 out, R3, R2, ground ball to OF fired home. R3 scores easily and R2 is thrown out at the plate. The B/R returns to the plate to pick up the bat and instruct R2 to slide. The pitcher sees the B/R's action and tells the catcher to fire the ball to 1B for an out. 2 outs?

I have not seen a ruling which states the B/R has no obligation to continue running to 1B when the 3rd out has been made on another runner.