While rotated test booklets have been employed in large-scale assessments to increase the content coverage of the assessments, rotation has not yet been applied to the context questionnaires administered to respondents. This paper describes the development of a methodology that uses rotated context questionnaires in conjunction with multilevel item response models and plausible values. In order to examine the impact of this methodology on the continuity of the results, PISA 2006 data for nine heterogeneous countries were rescaled after having been restructured to simulate the outcomes of the use of different rotated context questionnaire designs. Results revealed negligible differences when means, standard deviations, percentiles, and correlations were estimated using plausible values drawn with multilevel item response models that adopted different approaches to questionnaire rotation. The results of the analyses support the use of rotated contextual questionnaires for respondents in order to extend the methodology currently used in large-scale sample surveys.