In order to allow a single user registered on a single local host or other machine to access multiple shared resources on a remote host, an aliasing mechanism is employed so that multiple concurrent connections can be established by the user to a single remote host, with each connection using a different identity. Each connection can therefore be used to access a different shared resource on the remote host. In some illustrative examples, a user's identifier such as his or her machine log-in identification may be associated with two or more resource sharing aliases. As a result, two or more resource sharing sessions can be established by the user with a single remote host, with each of the sessions using a different one of the aliases. The resource sharing sessions are usually established in accordance with a resource sharing protocol such as the Server Block Message (SBM) protocol.