For the Love Level 3 event for Nami, you need to play version 0.3.7, complete the Level 3 event for Ash and have more than 20 coins. If all conditions are met, the event will start on Monday morning in the main character's room.
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The level 3 event for Ash is the initial event of the Third Act, after which level 3 events become available to other characters. It automatically starts on Saturday morning if you have completed the Level 2 event for Ash, the Major Event of the Second Act. You must also have ten or more Strength, Agility, and Endurance.