I suggest another tuning after the next change of season is well established. I say that the next tuning will last better, but this one will make the biggest difference.
I do between two and three passes, depending on the part of the scale. I'm not allergic to work the first time I see a piano. It gets the relationship off to an excellent start, which promotes trust and cordiality from then on. It's also a chance to deal with any little problems the piano is having, and to answer questions and deal with concerns the owner may have.
One thing about being 75 and semi-retired: I never need to rush to another job.