While I’m not familiar with SendGrid, there are a few email apps available in the Shopify App Store that allow you to fully customize your email notifications.
Two great examples of this are Mailchimp and Klaviyo. While Klaviyo won’t override the notifications and send them instead, they do provide you the code after you have finished customizing to add to your Shopify notifications. For full details on how this works, you can check out their guide here.
Speaking of notifications, these apps also let you create beautiful marketing emails. I would love to learn more about your current marketing strategy in regards to email campaigns! If you haven’t already, also make sure to check out our blog on 20 Email Marketing Best Practices to Turn Campaigns into Sales!