Suggestions for an eCommerce shopping cart which would allow multiple shipping tables to be setup?

We are currently using ECWID and are adding a new product to our online store. We are limited as to how we can customize our shipping tables and as a result shipping rates are being calculated on just one of our products.

This would be for a small business, any suggestions on what kind of eCommerce shopping cart would accommodate multiple shipping tables?

Magento, WooCommerce, and Shopify are the most widely used ecommerce platforms, and each of them can support complex shipping options.

Magento's Multiple Table Rates extension provides configurable shipping options, but it may be a more complex solution than a small business wants to take on.

WooCommerce's Table Rate Shipping extension provides configurable shipping options for Wordpress sites.

Shopify claims to support complex shipping rate requirements, but a quick web search will show you quite a few Shopify customer complaints about the added cost for some of the shipping functionality.