This paper presents a novel application of Alternating Structure Optimization (ASO) to the task of Semantic Role Labeling (SRL) of noun predicates in NomBank. ASO is a recently proposed linear multi-task learning algorithm, which extracts the common structures of multiple tasks to improve accuracy, via the use of auxiliary problems. In this paper, we explore a number of different auxiliary problems, and we are able to significantly improve the accuracy of the NomBank SRL task using this approach. To our knowledge, our proposed approach achieves the highest accuracy published to date on the English NomBank SRL task.