Windows does NOT allow you to establish multiple connections to the same server using more than one set of credentials. If you try, you receive:
System error 1219 has occurred.
The credentials supplied conflict with an existing set of credentials.
Microsoft claims that the only solution is to "disconnect the previous connection(s) to the server".
There is another solution!
You can make the connection using the IP address:
net use <Drive:> \\xxx.xxx.xxx.xxx\shareName Password /u:DifferentUserAccount