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Increasing the number of turns increases the magnetic field if the current remains constant. In your situation, you are postulating (implicitly) that the applied voltage is constant, and that the current is reduced. The product N⋅I is therefore unchanged, and the magnetic field does not increase when you increase the number of turns of a resistive wire.
Note - for some of the largest magnets used in medical imaging, they use superconducting wire.
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