Abstract Scalar invariance is an unachievable ideal that in practice can only be approximated; often using potentially questionable approaches such as partial invariance based on a stepwise selection of parameter estimates with large modification indices. Study 1 demonstrates an extension of the power and flexibility of the alignment approach for comparing latent factor means in large-scale studies (30 OECD countries, 8 factors, 44 items, N = 249,840), for which scalar invariance is typically not supported in the traditional confirmatory factor analysis approach to measurement invariance (CFA-MI). Importantly, we introduce an alignment-within-CFA (AwC) approach, transforming alignment from a largely exploratory tool into a confirmatory tool, and enabling analyses that previously have not been possible with alignment (testing the invariance of uniquenesses and factor variances/covariances; multiple-group MIMIC models; contrasts on latent means) and structural equation models more generally. Specifically, it also allowed a comparison of gender differences in a 30-country MIMIC AwC (i.e., a SEM with gender as a covariate) and a 60-group AwC CFA (i.e., 30 countries × 2 genders) analysis. Study 2, a simulation study following up issues raised in Study 1, showed that latent means were more accurately estimated with alignment than with the scalar CFA-MI, and particularly with partial invariance scalar models based on the heavily criticized stepwise selection strategy. In summary, alignment augmented by AwC provides applied researchers from diverse disciplines considerable flexibility to address substantively important issues when the traditional CFA-MI scalar model does not fit the data. Translational Abstract Determining whether people in certain countries score differently in measurements of interest (e.g., values, attitudes, opinions, or behaviors) can assist in testing theories, comparing countries, and advancing our psychological, sociological, and cross-cultural knowledge. Meaningful comparisons of means or relationships between constructs within and across nations require equivalent measurements of these constructs. However, tests of measurement equality or invariance usually fail when many groups are considered. Asparouhov and Muthén (2014) presented a new method for multiple-group confirmatory factor analysis (CFA), referred to as the alignment method. A strength of the method is the ability to estimate group-specific factor means and variances without requiring exact measurement invariance. Study 1 introduces an extension of the alignment method that can flexibly be applied in a large range of structural equation models. This is demonstrated by comparing latent factor means and relationships between 8 motivational constructs and covariates (e.g., gender) across 30 countries in a large-scale study (PISA, N = 249,840), in which the traditional measurement invariance was not achieved. Study 2, a simulation study, was presented showing that latent means were more accurately estimated with the alignment method than with other measurement invariance models (e.g., partial invariance models). In summary, the alignment method, augmented by its more flexible extension suggested in the present article, provides applied researchers from diverse disciplines considerable flexibility to address substantively important issues when the traditional measurement model does not fit the data.