Shape memory polymers can be fixed into a temporary shape and subsequently recover to its permanent shape when triggered by an external stimulus, typically heating. Recently, increasing attention have been focused on developing tunable triple- or even multi-shape memory polymers(MSMPs), which are believed to have a great potential for a wide range of applications, such as smart devices, sensors, actuators and biomedical products. Herein, we fabricated a tunable MSMPs with alternating multilayered structure consisting of poly (vinylidene fluoride) (PVDF) and poly (methyl methacrylate) (PMMA) via layer-assembly coextrusion technology. The number of layers was multiplied by combining an assembly of layer-multiplying elements with two extrudes, and induced the simultaneous increase of the shape fixing (Rf) and recovery ratios (Rr). For the specimen having 1024 layers, both of the Rf and Rr reached as high as above 90%, which is much better than the conventional PVDF/PMMA blends. In addition, numerous layer interfaces formed in the 1024-layer system caused a broad glass transition range (about 110℃), due to the interfacial diffusion between PVDF and PMMA layers. Consequently, the 1024-layer system exhibited good triple- or even quadruple-shape memory effect. The results achieved in this work reveal that the multilayered assembly provides a simple and efficient strategy to fabricate tunable MSMPs. Keywords: multi-shape memory polymers, multilayer structure, interface