Currently the way promo codes work, you cannot exceed the highest threshold tied to the promo.
For example, if I have a promo code saying to give a 5% discount on a $5,000 order, if a customer has $6,000 in their cart and try to use the promo code, it will say Invalid Promo Code.
It would be nice if the website would give the 5% discount on the first $5,000 and not discount the remaining $1,000. Instead, we have to tell our customers to place two orders. One with the discount and the remaining $1,000 without.