I crochet Amigurumi stuffed toys. I don't always have the color that a shopper is looking for. How do I set up so that they can order a specific color or maybe a boy doll or girl doll?
Sounds like you would need to manage this on a case by case basis.
Maybe add a section to the site that says "Item you wanted out of stock? Reach out to us directly for a special order" or something like that and have a button underneath that take them to a contact form they can fill out with the details you need. Then you can work directly with them to curate the order.
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