I'm sorry that you're facing such condition but as a community member I would like to share my experience with you.
I have one store and I added a drop-shipping company app to add their products on my store but as they've different shipping cost for each pincode/zipcode so I contact Shopify Support to add an add-on which is Carrier Calculated Shipping and that costed my $20 per month only and I'm now don't need to add any shipping rules on my store because using that add-on it's auto sync with dropshipping company's rules.
If this is what you're talking about you should talk with Shopify Support.
Let me know if you're talking something else.
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This is the problem... For months, I have read article after article about Shopify being able to add this for $20.00 a month and now they just don’t offer it.
Your choice is $299 for third party shipping or Pre Pay the ANNUAL fee for a Basic plan to get the shipping. So you have to fork out around $3700 dollars just to third party ship. If you have 2 stores this is slightly under $10000.
The big box stores already get a huge discount on their shipping rates, individuals can’t compete with those rates and now Shopify is sticking it to the small business person.