With American Express, there are a few limitations to product changes. The first one is that you cannot product change a cash back card to one that earns Membership Reward points. For example, you can't product change a Blue Cash card to an Everyday card.
The second rule is you can't product change a charge card to a credit card. This means that you can't product change an Amex Platinum card to an Everyday card. However, you can downgrade an Amex PRG or Platinum to the Green card.
You also can't product change a business card to a personal card. For example, you can't product change an Amex Business Platinum to a personal Amex Platinum card. Not being able to product change between business and personal cards is standard practice.
For co-branded cards, you can only product change within their respective group. For example, the Amex Delta Gold card can be product changed to any Amex Delta card.
Given these rules, this means there are limited downgrade and upgrade options. For example, the Amex SPG card doesn't have a product change option.
American Express often gives you promotions to upgrade from one card to a higher tier card. It may seem like a good offer, but once you upgrade, you will never qualify to get the signup bonus for the higher tier card. Amex has a once in a lifetime rule for signup bonuses, meaning you can't receive a signup bonus for a card you previously or already have.
When does it make sense to upgrade or downgrade?
With a card like the Amex Platinum card, there's not a free downgrade option. The Amex PRG and the Amex Green both have annual fees.
Regarding upgrades, the main reason to do it is if there's an offer attached and if it gives you increased value. For example, if you have the Amex PRG and you get an upgrade offer for the Amex Platinum, upgrading would save you a hard inquiry. I recommend this if you're inquiry sensitive and are applying for a mortgage or buying a car in the near future.
The other potential reason to upgrade is if the signup bonus for the card itself isn't worthwhile.