Understanding the interaction between nanoparticles (NPs) and cell membranes is crucial for the design of NP-based drug delivery systems and for the assessment of the risks exerted by the NPs. Recent experimental and theoretical studies have shown that cell membranes can mediate attraction between NPs and form tubular structures to wrap multiple NPs. However, the cooperative wrapping process is still not well understood, and the shape effect of NPs is not considered. In this article, we use large-scale coarse-grained molecular dynamics (CGMD) simulations to study the cooperative wrapping of NPs when a varying number of NPs adhered to the membrane. Spherical, prolate and oblate NPs of different sizes are considered in this study. We find that, in addition to tubular structures, the membrane can form a pocket-like and a handle-like structure to wrap multiple NPs depending on the size and shape of the NPs. Furthermore, we find that NPs can mediate membrane hemifusion or fusion during this process. Our findings provide new insights into the interaction of NPs with the cell membrane.