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Testing measurement invariance (MI) across multiple covariates (e.g., country, gender, age groups) is often of interest in applied research. Multiple group confirmatory factor analysis has been widely used to test MI for each covariate separately. By contrast, factor mixture modeling (FMM) and multiple-causes-multiple-indicators (MIMIC) model have the advantage of accommodating multiple covariates simultaneously and modeling potential interactions among covariates in terms of measurement noninvariance (MNI). This simulation study evaluates the performance of FMM and MIMIC in terms of accuracy in detecting MNI and identifying sources of MNI when there are multiple covariates. Preliminary results showed that MIMIC outperformed FMM. Practical recommendations will be provided for applied researchers who are interested in testing MI across multiple covariates.