Originally Posted by Bowgie

Some airlines sell international day of departure upgrades, but Delta is not one of them.

Since your first segment is on Delta, I'll assume this is a Delta-issued ticket. (If issued by KLM, call them). Call Delta reservations asap and ask them to "up-fare" you to either business class or Premium Select. You will be applying the cost you paid for the coach seat to the present-day price of the higher cabin price. There should not be a change fee, and I am assuming your original ticket was not a Basic or some kind of non-changeable ticket, just a regular Main Cabin fare. You can see for yourself what you'll be paying for that higher cabin fare by doing a trial booking on Delta.com for your same exact flights and dates.

Not sure if you mean Premium Select was not available when you originally booked (Delta flying an old non-PS plane then), or whether the price for it was too high. Either way, it does not matter now. Not sure if KLM has a Premium Select equivalent seat for the AMS-Dubai leg; check a seat map to see.