Modern computers are built with increasingly complex software stack crossing multiple layers (i.e., worlds), where crossworld call has been a necessity for various important purposes like security, reliability, and reduced complexity. Unfortunately, there is currently limited cross-world call support (e.g., syscall, vmcall), and thus other calls need to be emulated by detouring multiple times to the privileged software layer (i.e., OS kernel and hypervisor). This causes not only significant performance degradation, but also unnecessary implementation complexity.This paper argues that it is time to rethink the design of traditional cross-world call mechanisms by reviewing existing systems built upon hypervisors. Following the design philosophy of separating authentication from authorization, this paper advocates decoupling of the authorization on whether a world call is permitted (by software) from unforgeable identification of calling peers (by hardware). This results in a flexible cross-world call scheme (namely CrossOver) that allows secure, efficient and flexible cross-world calls across multiple layers not only within the same address space, but also across multiple address spaces. We demonstrate that CrossOver can be approximated by using existing hardware mechanism (namely VMFUNC) and a trivial modification of the VMFUNC mechanism can provide a full support of CrossOver. To show its usefulness, we have conducted case studies by using several recent systems such as Proxos, HyperShell, Tahoma and ShadowContext. Performance measurements using full-system emulation and a real processor with VMFUNC shows that CrossOver significantly boosts the performance of the mentioned systems.