Hi there Remy!
Don here from Shopify!
I had a quick look into this with our escalated team and confirmed by testing it myself; you (or a customer) should be able to apply more than one Gift Card code on one order at the checkout.
It would only be possible to use one discount code per order, though you should be able to first apply one gift card code and then another using the gift card/discount field during the checkout flow.
Check it out in your own store there if you wish to see it and should you encounter any sort of issue with this then just let us know here.
You can even email email@example.com and quote the ticket number you are given here so we can grab your email from the queue and look into this with you privately.
All the best!
We are currently able to enter only one gift card at a time. After entering a gift card, the entry field goes away.
We would like the entry field to remain so multiple gift cards can be entered.
We believe multiple gift card entry is supported by Shopify and will work if the field remains static.
Is there any way to show always the discount/gift card field?