Can you negotiate a title?

I applied to a job that has 'Senior' in front of the title and during the interviews, one of the questions they asked was about my years of experience because it was about 3 years lower than what they put in the job requirements. They asked me if I would still be open to a non-senior title because of that.

If an offer does come, would it be frowned upon to see if I could push for the senior title assuming the pay is aligned to what I am seeking? Everything else in the description looks to be aligned to my skillset & experience.

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