This study presents an examination of the transmission properties of multilayered partitions made up of multiple micro-perforated plates (MPPs) coupled to acoustic enclosures with general impedance boundaries. Multi-layered MPPs can lower the transmission while minimizing reflection in the source and receiving enclosure. Previous research has mainly focused on the double MPPs or triple MPPs partition itself. However, it is vital to analyze the in-situ sound transmission loss of the multi-layered MPP and their efficiency in a complex vibro-acoustic environment. The case when the multilayered MPPs are coupled to a receiving enclosure or coupled to both a source and receiving enclosure is investigated. The objective is to provide an analytical method to evaluate the transmission properties of multilayered MPPs coupled to acoustic enclosures while being computationally more efficient than the finite element method (FEM). Using the modified Fourier series for the acoustic pressure, a variational form for the acoustic and structure medium yields a completely coupled vibroacoustic system. A comparison between the sound transmission loss of the double MPPs, when mounted on an impedance tube and coupled to acoustics enclosures, shows the modal effect of the enclosures. The effect of enclosure shape, impedance boundary, perforation ratio, air gap thickness on the sound transmission properties of the double MPPs structure is examined for both cases. Finally, in both situations, the performance of triple MPP structure insulation is evaluated.