We address two persistent challenges in large-scale assessments of the Next Generation Science Standards: (a) the validity of score interpretations that target the standards broadly and (b) how to structure claims for assessments of this complex domain. The NGSS pose a particular challenge for specifying claims about students that evidence from summative assessments can support. As a solution, we propose tiered claims, which explicitly distinguish between claims about what students have done or can do on test items--which are typically easier to support under current test designs--and claims about what students could do in the broader domain of performances described by the standards, for which novel evidence is likely required. We discuss the positive implications of tiered claims for test construction, validation, and reporting of results.