By tailoring test forms to the test-taker's proficiency, Computerized Adaptive Testing (CAT) enables substantial increases in testing efficiency over fixed forms testing. When used for formative assessment, the alignment of task difficulty with proficiency increases the chance that teachers can derive useful feedback from assessment data. The application of CAT to formative assessment in the classroom, however, is hindered by the large number of different items used for the whole class; the required familiarization with a large number of test items puts a significant burden on teachers. An improved CAT procedure for group-based testing is presented, which uses simultaneous automated test assembly to impose a limit on the number of items used per group. The proposed linear model for simultaneous adaptive item selection allows for full adaptivity and the accommodation of constraints on test content. The effectiveness of the group-based CAT is demonstrated with real-world items in a simulated adaptive test of 3,000 groups of test-takers, under different assumptions on group composition. Results show that the group-based CAT maintained the efficiency of CAT, while a reduction in the number of used items by one half to two-thirds was achieved, depending on the within-group variance of proficiencies.