As Apple Inc. prepares to unveil both a new high-end iPhone and a cheaper version for the first time next week, it is already working on something bigger.

The electronics giant has begun evaluating a plan to offer iPhones with screens ranging from 4.8 inches to as high as 6 inches, people familiar with the matter say. That would be a sizable leap from the 4-inch screen of the iPhone 5 released last year, and, at the upper end, would be one of the largest on the market.

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