Stopping Harmful Offers on Platforms by Screening Against Fakes in E-commerce Act or the SHOP SAFE Act This bill makes an electronic commerce platform liable for infringement of a registered trademark 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 before the infringing act, including (1) requiring the seller to have a registered agent or a verified address 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 procedures for trademark owners to request the removal of listings for counterfeit goods, and (5) implementing policies to remove and ban repeat offenders. A person who knowingly makes a material misrepresentation in a request to a platform to take down a seller listing (because the listing allegedly uses a counterfeit mark and implicates health and safety concerns) shall be civilly liable to the seller injured by the resulting improper takedown. If a person makes 10 or more such improper takedown requests, the platform may sue on behalf of the sellers who consent to the platform's lawsuit. A party suing under this bill may choose to receive statutory damages (as opposed to actual damages) of $2,500-$75,000 for each improper request, depending on the circumstances of the case.