The effect that place Zushin Counter is once per turn, but only says "this card" instead of mentioning name, so if you have 3 copies of this card in your hand, you can place 3 Zushin Counters per turn, one for each copy of this card.
When you reshuffle in the copies, they're technically a new card when drawn, meaning if I had activated 3 copies of Zushin and placed 3 counters on one monster, reshuffled 3 Zushins into my deck and drew all 3 with a card like Mallet, I could place 3 new counters on my monster for a total of 6 counters in one turn.
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