Can I upgrade a previously purchased iPhone under the iPhone Upgrade Program? I bought an iPhone 6s Plus from Apple a couple of years ago. Can I enroll in the iPhone Upgrade Program and upgrade it to an iPhone 8/X?
Apple offers trade in for any phone you own outright. You have to pay monthly as part of an upgrade plan to get started, so unless you are paying Apple or the financing arranged through apple, you aren't part of the upgrade program which lets you get a new phone after 12 monthly payments.

You can easily check though - https://www.apple.com/shop/iphone/iphone-upgrade-program

I suppose it depends on what you mean by "upgrade" and what exact transaction you started a couple of years ago.