Recent developments in acoustic metamaterials have been centered on broadening attenuating bandwidths, particularly below 1000 Hz, and addressing manufacturing challenges. The concept of Multiresonant Layered Acoustic Metamaterials (MLAM) was introduced as a practical realization with notable advantages, not only in terms of performance but also regarding manufacturing issues [1]. In this work, we delve into the application of coupling mechanisms to extend the attenuation bandwidths of acoustic metamaterials further. Building upon the previously proposed MLAM design, we analytically and numerically investigate how these coupling mechanisms can produce novel sound transmission loss responses with multiple coupled peaks, surpassing the double-peak response achieved thus far. We demonstrate the feasibility of realizing these responses within the MLAM structure and employ a specifically tailored computational optimization strategy to generate optimized designs for diverse targeted applications [2]. This approach leverages coupling mechanisms to trigger multiple resonances, resulting in a broadband continuous frequency range of attenuation. The presented computational homogenization model is used to assess different MLAM configurations, evaluating the influence of the number of coupled resonating layers on sound transmission loss response. The results highlight the enhanced features obtained through coupling mechanisms, showcasing the MLAM technology's potential for an efficient, easy-to-manufacture solution to low-frequency sound insulation.