It has become a trend for clients to outsource their encrypted databases to remote servers and then leverage the Searchable Encryption technique to perform secure data retrieval. However, the method has yet to be considered a crucial need for replication on searchable encrypted data. It calls for challenging works on Dynamic Searchable Symmetric Encryption (DSSE) since clients must share the search capability of the encrypted data replicas and guarantee forward and backward privacy. We define a new notion called 'Keyword Search Shareable Encryption' (KS2E2E) and the corresponding security model capturing forward and backward privacy. In our notion, data owners are allowed to share search indexes of the encrypted data with users. A search index will be updated with a new search key before sharing to guarantee the data privacy of the source database. The target database also inherits data search efficiency along with the shared data. We further construct an instance of KS2E called Branch, prove its security, and use real-world datasets to evaluate Branch. The evaluation results show that Branch's performance is comparable to classical DSSE schemes on search efficiency and demonstrate the effectiveness of searching encrypted data replicas from multiple owners.