Discussions on WooCommerce is off-topic here, but can’t resist myself answering. I faced a similar issue couple of months back and my solution was something like this.
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Remove the default add to cart form and variation choices in single variable product page. You can use JS or modify the template.
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Add custom form with checkboxes and quantity input for each variation
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Add those checked variations programmatically using
woocommerce_add_to_cart
hook.