Background: This paper extends a recent study by Kaplan and Su ("J Educ Behav Stat" 41: 51-80, 2016) examining the problem of matrix sampling of context questionnaire scales with respect to the generation of plausible values of cognitive outcomes in large-scale assessments. Methods: Following Weirich et al. ("Nested multiple imputation in large-scale assessments." In: "Large-scale assessments in education," 2. http://www.largescaleassessmentsineducation.com/content/2/1/9, 2014) we examine single + multiple imputation and multiple + multiple imputation methods using predictive mean matching imputation under three different context questionnaire matrix sampling designs: a two-form design studied by Adams et al. ("On the use of rotated context questionnaires in conjunction with multilevel item response models." In: "Large-scale assessments in education." http://www.largescaleassessmentsineducation.com/content/1/1/5, 2013), a three-form design implemented in PISA 2012, and a partially-balanced incomplete design studied by Kaplan and Su ("J Educ Behav Stat" 41: 51-80, 2016). Results: Our results show that the choice of design has a larger impact on the reduction of bias than the choice of imputation method. Specifically, the three-form design used in PISA 2012 yields considerably less bias compared to the two-form design and the partially balanced incomplete design. We further show that the partially balanced incomplete block design produces less bias than the two-form design despite having the same amount of missing data. Conclusions: We discuss the results in terms of implications for the design of context questionnaires in large-scale assessments.