Accurately predicting failure in woven composites requires knowledge of the stress states of the individual constituents that exist within the composite. Multicontinuum Technology provides a computationally efficient way of extracting constituent stresses and strains from a structural-level finite element analysis. Multicontinuum Technology was originally developed for composite materials consisting of two constituents. More recently, it was expanded to enable the extraction of stresses and strains of three constituents for the analysis of a plain weave composite. The present study is to investigate the value in extending the capabilities of Multicontinuum Technology to handle materials with complex heterogeneity that could benefit from the definition of many constituents. To determine the feasibility of this extension, a meso-scale finite element model of a triaxial braid was developed and used as a test case. The approach also included a finite element micromechanics model employed at the fiber-matrix level. Results produced by the models were validated by comparisons to experimental data of effective elastic constants of the material and initial failure loads. The model’s predictions of initial matrix failure were in very good agreement with the limited experimental data. Also, trends predicted for multi-axial load cases are in line with physically intuitive expectations. These results show promise for the success of future research in extending Multicontinuum Technology for application to composites with complex multiscale heterogeneity.