From the reference list, we have multiple others (some overlapping King vs Queen nomenclature):

King Midas: 3584, 4012, 4014, 4015, 4016, 4017, 4031, 4126, 4127, 4151, 4153, 4312, 4316, 4342, 4344, 4609, 4611, 4620, 4912, 5038, 5072, 9903
Queen Midas: 3585, 4313

Detailed listings for each are scarce in standard sources, but collectively:

• Design: Similar angular asymmetrical/Parthenon-inspired case and integrated gold bracelet.
• Movement: Manual-wind calibers (650 or 651).
• Collectibility: Rare; each is uniquely collectible due to low production and aesthetic distinction