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Data integrity is the most important factor when you are switching eCommerce platforms. If you lose your customer database or order history, you are basically starting your business from scratch. I always recommend using a service that offers a migration preview so you can audit the results before the final go-live. You can check out the service at https://www.shopping-cart-migration.com/ as they are quite advanced in how they handle complex database structures. We used their CSV file migration option for a custom legacy site and it worked without a hitch.