Even though the launcher supports multiple accounts and multiple profiles, it fails in the ability to have multiple sessions, with each new session overwriting the previous session's data, or otherwise rendering clients that logged in before unable to access their respective session data. This makes it impossible to have multiple instances of the Minecraft client running at the same time in a sane and stable fashion.
The launcher does have a way to do this, albeit unsupported as far as I know. If you use the -workDir option you can have multiple instances. eg: Minecraft.exe -workDir C:\Minecraft