Commodity processor architectures are releasing various instruction set extensions to support security solutions for the efficient mitigation of memory vulnerabilities. Among them, tagged memory extension (TME), such as ARM MTE and SPARC ADI, can prevent unauthorized memory access by utilizing tagged memory. However, our analysis found that TME has performance and security issues in practical use. To alleviate these, in this paper, we propose CoMeT, a new instruction set extension for tagged memory. The key idea behind CoMeT is not only to check whether the tag values in the address tag and memory tag are matched, but also to check the access permissions for each tag value. We implemented the prototype of CoMeT on the RISC-V platform. Our evaluation results confirm that CoMeT can be utilized to efficiently implement well-known security solutions, i.e., shadow stack and in-process isolation, without compromising security.