Yes, Magento 2 Gift Card Extension allows you to apply multiple coupon codes during checkout.

Read this guide on How to Configure Gift Card Extension in Magento 2 to setup this extension.

Here are the few more resource to help you get most out of this Gift Card Extension for Magento 2.

• How to Create a Gift Card in Magento 2
• Drive More Sales with eCommerce Gifting & Promotion Strategy
• Boost your Holiday Season Sale & Customer Retention with Magento 2 Gift Cards
• Prepare your Magento Store for Holidays with Gift Card and Gift Wrap Extensions