I can't imagine they do, although in a perfect world I would hope the grading companies would do this and also communicate with the other grading companies to help police things.
But PSA is a part of a publicly held company and their goals are aligned with profits for their shareholders. Just off the cuff, if PSA did have a database and checked crossovers, it would cut into their profits:
It's been reported PSA grades 2 million cards in a year. Obviously a small percentage would be crossovers, so let's assume this is only 1% of their total card submissions. That's 20,000 crossovers per year. If a grader/employee spends an average of 30 seconds to check a database and/or input card information to that database per card, that's 600,000 seconds per year, which is 10,000 hours, which is the equivalent of 5 full time employees working 40 hours per week for a year.
Even if I've over estimated, that still isn't happening.
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