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The tunability of magnetorheological elastomers is critical in diverse engineering applications where adaptive vibration control and isolation capabilities are demanded, such as for civil structures during seismic events and for vehicle systems. Traditional magnetorheological elastomers are limited by the applied magnetic field strength and a saturation threshold of ferromagnetic particle filler to produce significant tuning of properties. To enhance the adaptation of static and dynamic properties using magnetorheological elastomers, magnetoelastic metamaterials were recently investigated which leverage the combined influences of applied magnetic fields and the reconfiguration of internal void architectures controlled by combined magnetic field and strain field application. The concept of magnetoelastic metamaterials provides an innovative technique to control the material system properties in real-time. Yet, apart from the first demonstration of potential, the opportunity to fully exploit the internal void architectures remains unfulfilled since there is no conclusive understanding on relations among the internal void architecture geometries and the application of strain. Therefore, this research seeks to undertake a rigorous experimental and computational effort to comprehensively explore the interactions among metamaterial cellular void architectures to illuminate best means to tailor static and dynamic properties. For this topological study, the cellular structures are constructed with single or multiple layers of connected cross beams that included uniform and graded thicknesses of 0.80 mm, 1.00 mm and 1.20 mm. These geometries are also studied through an individual unit cell on which the entire architecture is based upon. After these specimens are fabricated, the mechanical properties are then characterized through quasi-static compression. Experimentations and simulations data analysis demonstrated a series of geometric designs that collapse at multiple critical strains during compression. By systematically configuring the preliminary geometric design, critical strains and local stiffness changes around layer collapse are accurately controlled. Through unit cell periodicity and strategic acrylic inserts, it is shown that collapse behaviors could further be controlled to exhibit stress distributions and collapse profiles similar to theoretical unit cell behavior. This understanding will guide future work to establish multiphysics modeling that illuminates the inner working mechanisms of properties tuning in magnetoelastic metamaterials.