Stopping Harmful Offers on Platforms by Screening Against Fakes in E-commerce Act of 2020 or SHOP SAFE Act of 2020 This bill establishes that an electronic commerce platform shall be liable for trademark infringement by a third-party seller of goods that implicate health and safety unless the platform takes certain actions. Specifically, the platform may be contributorily liable if the seller uses a counterfeit mark in connection with selling, offering, or advertising such goods on the platform. The platform may avoid such liability by taking certain actions, including (1) requiring the seller to be available for service of process in the United States, (2) verifying the seller's identity and contact information, (3) requiring the seller to agree to not use counterfeit marks with goods sold on the platform, (4) implementing technical measures to prescreen listings on the platform and remove listings for goods being sold with a counterfeit mark, and (5) implementing policies to remove and ban repeat offenders.