Yes--there's no limit to how many players can be substituted at once. Also, in the National League (or any league where pitchers have to bat) a team can make a "double switch", which in the case of a pitcher and catcher would result in the new pitcher batting in the previous catcher's spot in the batting order, and the new catcher in the pitcher's spot (probably ninth).
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The starting pitcher and any substitute must pitcher to a minimum of one batter, or have an Out made, before he can be replaced. Other than that, the Manager can change the pitcher whenever he wants to.
Teams in the Major Leagues can change pitchers as much as they want to in a game but any pitcher that comes in is required to face a minimum of one batter before they can be taken out of the game for a new Pitcher.
Inning---but not during an at bat. Although ambidextrous pitchers are extremely rare.