Can there be multiple chains in a showdown, and how do actions vs reactions work with chains?

Ruling: You can have infinite chains in a showdown, but only one chain at a time. Actions can only be used to start a chain (not in response to an existing chain), while reactions can be played whether or not there is a chain.

Sequence:

• A player with focus plays an action spell to start a chain
• Once a chain exists, only reaction speed effects can be added to it
• Both players pass priority in order without adding to the chain
• The chain resolves
• The next player gets focus and can start a new chain with an action
• The showdown only ends when both players pass focus in order without creating a chain

Nuances:

• You can never have more than one action spell on a single chain
• During combat with attacker/defender triggers on the initial chain, you cannot play action spells during that time