Stacking sounds like a cheat code and occasionally it is. Most of the time the store has already closed the gaps. Here is what still works.
Store coupon plus bank offer
This is the combination that survives on most platforms. The store code comes off the cart, then the bank discount comes off at payment. Read the minimum cart value on both — they are rarely the same number.
Cashback on top
Cashback sites pay out on the amount you actually paid, so a bigger coupon means a smaller cashback. The two together still beat either alone, but the maths is not additive.
What almost never works
Two store coupons on one order. A new-user code on an account with order history. A code from a different country’s storefront. Sites check all three.
Test in this order
Add to cart, apply the store code, then pick the card. If the bank discount vanishes when you apply the code, you have hit a stacking block and you need to pick the larger of the two.