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I recently sent out 11 of my applications with a good version of my personal statement, but while working on my last batch I made a few improvements that make my PS really great. The revised version more clearly describes my passion to study law. Should I resubmit the later version to the first 11 schools, or just go with it?

As long as your subject matter isn't off-putting in the first version, you're fine. Minor changes won't matter.