Generally not. Most of the discount codes that we accept, including student and staff discount, will only apply one per order, and will not apply against items that have already been discounted.
If you have a promo code for free delivery however, it is likely that this will also work alongside a promotional discount.
Always enter promotional codes separately in the promo box before checkout. If you are trying to apply a promo code and it's not working, check out the info here.