Can my iPhone 11 Pro Max support the newest iOS update?

Yes. iOS 17 is the latest major version of iOS, and your phone is on its compatibility list.

iPhone models compatible with iOS 17 - Apple Support

For help with updating, see:

Update your iPhone or iPad - Apple Support

Updating iOS: common issues and solutions - Apple Community

Hello kenni274, YES. The oldest iPhone supported on the new iOS 17.4 is iPhone SE 2nd Edition, so your good on your iPhone 11 PM.