How do multiple branches from one node occur with the Monte Carlo Tree Search?
It sounds like you're reading a summary/overview.  You might be reading too much into one sentence there.  The sentence says "MCTS will add one child node per iteration".  That doesn't mean each node will have only one child after the process finishes.  You might have one iteration that adds one child of X, and a later iteration that adds another child of X, and an even later iteration that adds yet another child of X, and so on.

Similarly, nothing says that MCTS is limited to adding only two or three children per node.