Extending the single-user searchable symmetric encryption (SSE) immediately to the multiuser scenario is not straightforward. In the multiuser scenario, recipients cannot safely achieve multisearchable computing without using a third party or specified users, which diminishes the application's utility. Moreover, there are two issues related to pattern privacy and file updating: One is that the majority of extant SSEs only emphasize the privacy of a partial pattern (one of the search/access/size patterns), resulting in information leakage. The second issue is that, with the exponential expansion of the number of files, it is unclear how to achieve unrestricted index capacity management while efficiently updating the encrypted index. To overcome the aforementioned issues, we offer a general dynamic named $G$-$DSSE$, that is blended with the pseudorandom function and the integer vector homomorphic encryption. Combining $k$-anonymity and delayed write-back techniques, $G$-$DSSE$ can realize multisearchable computing without relying on a third party while simultaneously guaranteeing multiple patterns and greater forward/backward privacies. The combination of $k$-anonymity and delayed write-back solves the unnecessary waste of communication overhead and the problem of pattern leakage in extreme cases. $G$-$DSSE$ achieves noninteractive update, even batch update, and nonrestrictive index capacity management in the encrypted index. Meanwhile, it can be expanded flexibly to ensure the precision and integrity of search results.