Interaction effects are ubiquitous in social science research, and detecting them in data is an important goal for many researchers. In linear regression, where all variables are observed, we can represent an interaction effect simply by adding an interaction term that multiplies the two variables of interest. Unfortunately, when variables are latent, including interaction effects in the model is far from trivial. In this project, we exploit the two-stage nature of the structural-after-measurement (SAM) framework to easily include latent interaction and quadratic terms. The goal of the project is 1) to refine and simplify the expressions for the augmented summary statistics of the latent variables, 2) to derive new formulas to compute two-step corrected standard errors, 3) to test the method and to compare it to other methods in a large simulation study, and 4) to implement the technology in the open-source R package lavaan.