The checkout permalink works with multiple discount codes separated by commas, e.g. ?discount=DISCOUNT1,DISCOUNT2. If you append this to your cart form action (e.g. /cart?discount=DIS1,DIS2`), when submitting cart to proceed to checkout, it will apply the discounts.
For the /discount/ solution, I tried /discount/DISCOUNT1+DISCOUNT2 and /discount/DISCOUNT1,DISCOUNT2 and /discount/DISCOUNT1&DISCOUNT2 but none worked, so I suspect this solution is only for singular discounts.
Same goes for the discount_code cookie, singular only in my testing.
The above is unconfirmed from Shopify, just via experimenting.