Yes and no. You don't develop physical tolerance, but you know what to expect, reducing anxiety. Experienced clients handle sessions better because they've learned to relax, breathe through it, and understand the sensation isn't dangerous.
There's no physical adaptation—your nerve endings don't become less sensitive with more tattoos. However, the psychological component changes dramatically. First-time clients often experience significant anxiety: what will it feel like? Can I handle it? Am I going to embarrass myself? This anxiety amplifies pain perception. By your second or third tattoo, you know exactly what to expect. The mystery is gone, and with it, much of the fear-based amplification. You've proven to yourself that you ca...
Pro Tip: If your first tattoo was on an easy placement, don't assume your second will feel the same if it's on a challenging spot. Ribs hurt more than forearm regardless of how many tattoos you have.