How many times can the infield meet at the mound without the coach?

Once per inning. Under Rule 3-4-6, each team on defense gets one player-to-player meeting per inning. A meeting is any gathering of two or more defensive players, such as the catcher going out to talk to the pitcher. The umpire will deny any further requests that half-inning.

These are not player meetings:

• talking with the pitcher after warm-up throws at the start of a half-inning, or after a relief pitcher's warm-ups
• a fielder handing the ball to the pitcher with a quick word after an out
• gathering while play is stopped for an offensive conference or an injury

A visit by a coach is a separate charged conference. If the coach comes out while the catcher is still at the mound, it counts only as a charged conference. If the coach comes out and changes pitchers, it's neither.