[mikech]

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OK, first off, how does the order go? Does the batter have to switch first or does the pitcher have to swtich first? Or either way?

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the batter has to be announced first. i've often seen a manager wait until the pinch-hitter is announced, and THEN go out and replace his pitcher.

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Does it ever go change-change-change? Like, a new lefty come in, so a pinch-hitter replaces the batter, then a righty comes in.

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i think JoA is right on this one, the pitcher has to face a batter, so a sequence of reliever/pinch-hitter/new reliever can't happen.

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Or, a pinch-hitter comes in, the pitcher switches, then a different pinch-hitter comes in.

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yes, i've seen this. this is why the pitcher's manager will wait for the new batter to be announced, so if the opposing manager still wants a favorable lefty-righty matchup, he'll have to burn a pinch-hitter.

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Anyway, just wondering if is is allowed, and if so, if teams ever do two switches in a row where the first switched guy doesn't even play.

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burning a pinch-hitter is allowed, and although it's rare, i've seen it happen.