The present work deals with multi-layer rectangular core topology systems built up by stacking layers made of different rectangular core geometries. Multi-layer systems have been intensively studied in terms of mechanical performances whereas their vibroacoustic behavior, acoustic efficiency and design is however still an open issue. Several design parameters should be considered to fully understand the dynamic and acoustic behaviour of such structures. Therefore, this paper focuses on controlling the transition frequency and the Sound Transmission Loss (STL) by modifying geometrical parameters of the unit cell, while keeping the mass constant. Infinite panels and real wavenumbers will be considered in the study. The Wave Finite Element Method (WFEM) is used to obtain the targeted indicators. The proposed designs give the opportunity to shift the transition frequency and to control the flexural waves propagating in the structure. Besides, the STL is highly improved in the full frequency range of interest compared to a standard sandwich panel made of a single core.