Stand by your Oil Pollution Act or the STOP Act - Amends the Oil Pollution Act of 1990 to: (1) extend liability to any corporation, partnership, or other person (other than an individual) having an ownership interest exceeding 25% in any responsible party; and (2) limit such an entity's liability with respect to an incident (any occurrence or series of occurrences having the same origin, involving vessels and facilities, resulting in the discharge or substantial threat of discharge of oil) to no more than the percentage of the entity's aggregate ownership interests in all other responsible parties with respect to such incident.