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Yes, 'While blocking' is ongoing phrasing. You can choose to manually trigger Herod's Dungeon as many times as the conditons are met.
what would that accomplish?
no, because herodias' trigger happens before herod antipas'.
herod antipas -> herodias + empty dungeon: capture heroherod antipas -> herodias + occupied dungeon: discard captured hero, capture herosalome -> herod + empty dungeon: capture herosalome -> herod + occupied dungeon: discard captured hero, capture heroits the exact same.
Bump, has there been an official ruling on this?