Can I update my iPhone 7 Plus to iOS 16?

No. An iPhone 6s, iPhone 6s Plus, iPhone 7, iPhone 7 Plus, or iPhone SE 1 isn't capable of 16 or above; they require an A11 or better CPU.

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Can I update to 16?

No

You will need an iPhone 8 or higher model to run iOS 16.

You will need an iPhone XR or higher model to run iOS 17.