Recent advances in deep foundation models have led to a promising trend of developing large recommendation models to leverage vast amounts of available data. However, we experiment to scale up existing recommendation models and observe that the enlarged models do not improve satisfactorily. In this context, we investigate the embedding layers of enlarged models and identify a phenomenon of embedding collapse, which ultimately hinders scalability, wherein the embedding matrix tends to reside in a low-dimensional subspace. Through empirical and theoretical analysis, we demonstrate that the feature interaction module specific to recommendation models has a two-sided effect. On the one hand, the interaction restricts embedding learning when interacting with collapsed embeddings, exacerbating the collapse issue. On the other hand, feature interaction is crucial in mitigating the fitting of spurious features, thereby improving scalability. Based on this analysis, we propose a simple yet effective multi-embedding design incorporating embedding-set-specific interaction modules to capture diverse patterns and reduce collapse. Extensive experiments demonstrate that this proposed design provides consistent scalability for various recommendation models.