There are two specific settings in the AnyConnect profile that can allow or disallow you to perform what you need:
1. Windows VPN Establishment which can be set to "Local Users Only" or "Allow Remote Users"; assuming you chose the second option, you'll be allowed to use a remote user
2. Windows Logon Enforcement which can be set to "Single Local Logon" or "Single logon"; assuming you choose the second option, you'll be allowed to use a remote user, but none of the options allows multiple logons, which is your problem
There is one fix for this though, by using the AnyConnect Management Tunnel function, which by the name, i guess it was designed for engineer to manage stuff. With this functionality, Windows Logon Enforcement is disabled and Windows VPN Establishment is unconditionally set to "Allow Remote Users". Look in the AnyConnect Configuration Guide for the "Management Tunnel".