Most CAT has been studied under the framework of unidimensional IRT. However, many psychological variables are multidimensional and might benefit from using a multidimensional approach to CAT. In addition, a number of psychological variables (e.g., quality of life, depression) can be conceptualized as being consistent with a bifactor model (Holzinger & Swineford, 1937) in which there is a general dimension and some number of subdomains with each item loading on only one of those domains. The present study extended the work on the bifactor CAT of Weiss & Gibbons (2007) in comparison to a fully multidimensional bifactor method using multidimensional maximum likelihood estimation and Bayesian estimation for the bifactor model (MBICAT algorithm). Although Weiss and Gibbons applied the bifactor model to CAT (BICAT algorithm), their methods for item selection and scoring were based on unidimensional IRT methods. Therefore, this study investigated a fully multidimensional bifactor CAT algorithm using simulated data. The MBICAT algorithm was compared to the two BICAT algorithms under three different factors: the number of group factors, the group factor discrimination condition, and estimation method. A fixed- test length was used as the termination criterion for the CATs for Study 1. The accuracy of estimates using the BICAT algorithm and the MBICAT algorithm was evaluated with the correlation between true and estimated scores , the root mean square error (RMSE), and the observed standard error (OSE). Two termination criteria (OSE = .50 and .55) were used to investigate efficiency of the MBICAT for Study 2. This study demonstrated that the MBICAT algorithm worked well when latent scores on the secondary dimension were estimated properly. Although the MBICAT algorithm did not improve the accuracy and efficiency for the general factor scores compared to two BICAT algorithms, the MBICAT showed an improvement of the accuracy and efficiency for the group factors. In the two BICAT algorithms, the use of differential entry on the group factors did not make a difference compared to initial item at trait of 0 for both the general factor and group factor scales (Gibbons, et al., 2008) in terms of accuracy and efficiency.