Apple is looking to squeeze a further $707m (£437m) out of Samsung on top of the $1bn it was awarded last month.
The iPhone maker is locked in a bitter smartphone patent battle in 10 countries and is looking to get a total of 21 products banned from sale in the US which it claims infringes its patents, including the flagship Galaxy S3 handset.
Apple said in an earlier submission: "Samsung has systematically copied Apple's innovative technology and products, features and designs and has deluged markets with infringing devices in an effort to usurp market share from Apple.
"Instead of pursuing independent product development, Samsung slavishly copied Apple's innovative technology, with its elegant and distinctive user interfaces product design, in violation of Apple's valuable intellectual property rights," it added.
In a motion filed late last week, Apple sought a further $400m damages award for design infringement by Samsung; $135m for 'wilful infringement' of its utility patents, $121m in supplemental damages based on sales not covered during the jury's deliberation, and $50m of prejudgement interest on damages.
According to a statement in a Reuters article, Apple is demanding that the injunction covers "any of the infringing products or any other product with a feature or features not more than colorably different from any of the infringing feature or features in any of the infringing products".
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