'Avenger II' was an Allied supplement to 'Avenger' (ii), and as such a cover plan designed to confuse the Germans as to whether the Allies intended to make their main thrust into Germany in the north or in the south (November 1944).
The 'Avenger II' plan added to the basic 'Avenger' (ii) scheme the notion that the fictitious British 4th Army was being readied in the eastern part of the UK to descend in an amphibious landing on the north coast of Germany.
The plan was stillborn for the same reasons as 'Avenger' (ii).