Customize New Tab button functionality

The new tab (+) button appears to simply start a new instance of the exe running in the current window. To see how undesirable this can be, try using it to start a new PowerShell session and see your font get huge (because the font and other settings belog to the shortcut to PowerShell.exe, not PowerShell.exe itself). Worse still (though in a much less commonly used program) in MinTTY the new tab button adds a new icon to my Taskbar rather than starting another process under the same icon.

I would like it if the New Tab button acted just like Shift Clicking the icon of the running process in the Taskbar, thus duplicating all the flags sent to the new process by the shortcut that's in the Taskbar. This would solve both of these issues. Allowing the user to specify which shortcut to use for a process would also be helpful, but not quite as good as I may have two shortcuts for the same exe.