In computerized adaptive testing, item exposure control methods are often used to provide a more balanced usage of the item pool. Many of the most popular methods, including the restricted method (Revuelta and Ponsoda), use a single maximum exposure rate to limit the proportion of times that each item is administered. However, Barrada et al. showed that by using multiple maximum exposure rates, it is possible to obtain an even more balanced usage of the item pool. Therefore, in this paper, we develop four extensions of the restricted method that involve the use of multiple maximum exposure rates. A detailed simulation study reveals that (a) all four of the new methods improve item pool utilization and (b) three of the new methods also improve measurement accuracy. Taken together, these results are highly encouraging, as they reveal that it is possible to improve both types of outcomes simultaneously.