Fabrication of terahertz modulators as simple devices with high modulation depth across a broad bandwidth is still very challenging. In this study, four different chemical vapor deposition grown multilayer graphene (MLG) modulators based on MLG/ionic liquid/gold sandwich structures have been investigated. Flexible substrates (PVC and PE) were chosen as host materials, and devices were fabricated with three different thicknesses. The resultant MLG devices can be operated at low voltages between 0 and 3.4 V providing nearly complete modulation between 0.2 and 1.5 THz with low insertion losses. Even with such low gate voltages, the devices have been doped significantly inducing 7-11-fold improvement in their sheet conductivities depending on device thickness. In addition, sheet conductivity has been improved more than three times as the graphene layer number increased from 30 to 100. With the demonstration of promising device performances, the proposed modulators can be potential candidates for applications in terahertz and related optoelectronic technologies.