Yes.  The common method is to retain completely separate databases for each institution, but allow staff a centralized access point to move in and out of each credit union database to perform needed tasks.  

For example, CU*Answers and Xtend have been able to create great operational efficiencies using this configuration method for shared bookkeeping, member communications, web hosting, and many other functions.  Visit the Developer's Help Desk if you would like to talk to someone about a potential project.