Note: This information is for advanced users only.
In build 1.2.5427.16 (latest patch, as of this post), you can patch the bytes in MassEffect3.exe at file offset 0x1518AEC from A0 7B 6B to 60 31 D6 to enable the console. Note that there will be no output from your commands, but they will work (if properly entered).
For example, from the main menu, try the command open BioP_MPNov.
Obviously, you should not play multiplayer with this edit.