Multi-head self attention provides strong representational performance but is computationally expensive, which limits its applicability in low-resource environments. Although Multi-Head Latent Attention alleviates the key-value cache bottleneck by compressing representations into a latent space, model training remains computationally demanding, particularly under resource constraints. Our objective is to further reduce the number of learnable parameters in Multi-Head Latent Attention by pre-multiplying the query and key weights, since these matrices are ultimately multiplied during attention computation and by introducing a modified architecture that incorporates a latent space for both the queries and key-value latent representation weights. We refer to this approach as Multi-Head Multi-Latent Attention (MMLA). The experimental results indicate a performance comparable to MSA, accompanied by a 47% reduction in training time. These findings suggest that MMLA not only achieves superior efficiency but also outperforms models with comparable parameter counts, positioning it as a more cost-effective and computationally practical alternative to existing attention mechanisms.