Designing an effective K-12 alternate English language proficiency assessment (ELP) for English learners with significant cognitive disabilities (ELSCDs) is a substantial undertaking, particularly given the absence of design models for such an assessment and limited empirical research to guide test design teams. These challenges emphasized the need to follow a rigorous and principled approach in order to establish an appropriate design. This paper describes how Evidence-Centered Design (ECD) -- a comprehensive and flexible assessment design framework -- was applied throughout the design process of such an assessment. By extending the principles of ECD, a maximally accessible alternate ELP assessment was designed and implemented, and evidence was collected to support validity. Implications for this assessment design effort include findings for the education and assessment of ELSCDs, the application of ECD to the assessment of diverse test takers, and to a general movement in the field toward more personalized assessments.