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You will also need to insert additional entries to the core_config_data table. If you've got one site already, you'll see one entry each for "web/unsecure/base_url" and "web/secure/base_url" in that table. Add 2 more entries for "web/unsecure/base_url" and "web/secure/base_url" with scope_id set to the related store_id found in the core_store table. Update their values to the new store URL.

I've only been working with Magento for 3 days, so there may be a better/proper way of doing this so feel free to suggest an alternative :)