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This paper presents the current and thermal phenomena of multi-stacked No-Insulation (NI) REBa2Cu3O7-x (REBCO, RE = Rare Earth) pancake coils during a local normal-state transition. An NI winding technique is expected to enhance the thermal stability of REBCO pancake coils, and it was verified in numerical simulations on a single pancake coil. However, a multi-stack of pancake coils are used to generate a high magnetic field in practical applications. When a normalstate transition occurs in one of multi-stacked pancake coils, it may deteriorate the stability of the other pancake coils. Therefore, we have developed a numerical simulation code to clarify the current and thermal behaviors of multi-stacked NI REBCO pancake coils using a partial element equivalent circuit model and a thermal finite element method.