The traditional approach to studying student understanding presents a question and uses the student's answer to make inferences about their knowledge. However, this method doesn't capture the range of possible alternative ideas available to students. We use a new approach, asking students to generate a plausible explanation for every choice of a multiple-choice question, to capture a range of explanations that students can generate in answering physics questions. Asking 16 students to provide explanations in this way revealed alternative possibilities for student thinking that would not have been captured if they only provided one solution. The findings show two ways these alternatives can be productive for learning physics: (i) even students who ultimately chose the wrong answer could often generate the correct explanation and (ii) many incorrect explanations contained elements of correct physical reasoning. We discuss the instructional implications of this multiple-choice questioning approach and of students' alternative ideas.