Some background on COSSAC & the earlier invasion plans might be usefull here. COSSAC was formed as one of the agreements of the January 1943 Cansalblanca confrence & General Morgan appointed as Chief of Staff of COSSAC. This was never more than a planning staff. COSSAC had no commander, no combat or support units & reported to the Allied Combined Chiefs of Staff. Morgans writ fell into two parts. He was to prepare plans for invading NW Europe based on only the Allied forces actually in the UK. this limit was important. Morgan was to prepare information and estimates for larger forces, but specific plans for only what was at hand.
http://www.ibiblio.org/hyperwar/USA/USA-E-Supreme/USA-E-Supreme-5.html
The principle limit the COSSAC staff faced was landing craft. 1943 operations in the Mediterranean & MacAurthurs South Pacific offensive drew the bulk of the production and little was sent to the UK. In January of 1943 there were suffcient landing craft for a single division size assualt & limited follow up of about two divisions & corps units per week. Expansion to a three division assualt was slow and was based on planned deliveries of landing craft. The Combined CoS agreed on enough boats to be sent to the UK to expand training, and to accomodate the various Sledgehammer, Roundup, Rankin, & early Overlord plans.
When SHAEF was stood up at the end of 1943 COSSAC was dissolved & its staff distributed to SHAEF, 21 Army Group, 12 Army Group, and elsewhere. General Morgan became Deputy Chief of Staff at SHAEF. Butcher who Ike wanted for his CoS knew nothing about the Overlord plans as he had been entirely involved in Mediterranean operations for over a year so it was logical to bring Morgan and his library of intelligence on German forces, terrain information, estimates, ect... into SHAEF to continue doing what he had been doing. Montgomery certainly deserves a great deal of credit for the Neptune/Overlord plans of 1944. But, Morgans continued role on the staff at SHAEF during those preperations has been largely ignored.
I can't find a reference to the make-up of the thre divisions of early Overlord. Anyone? A guess would be 2 British, one American, but I can't find anything.
Call it Overlord 1.0 ? Nominally the three assualt groups were to be one Brit, Canadian, US each. The beaches were to be Omaha, Juno, & IIRC Gold.
Mony and Ike shot it down and basically told their political masters that the necessary landing craft just had to be found. period. Probably the only time Ike and Monty agreed on anything.
The Combined CoS had seen Morgans estimates for larger invasion requirements long before Ike & Monty departed the Med. The bulk of new construction were scheduled for delivery to the UK, as were most of those in the Med. The political master interfering was Churchill who continued insisting on large scale amphibious ops in the Balkans. marshall was dead set against anything that interfered with Overlord and ran sucessfull interferance for Ike against Kings & MacAurthurs requests for the PTO.
I am not sure how well-defined Morgan's air plan was and whether he also got Ramsey and RN deeply involved before Monty took over.
Few clues here. Ramsey was commanding in the Med until January 1944 & so would have had nothing to do with Morgans 1943 plans. Morgan wrote plans based on what was at hand, but he had zero command authority, and little interest from Churchill. Given the huge number of air groups destined for the UK, & over 10,000 operational in December 1944 Morgan may have been planning on substantial support from the Brit tactical airforces, the US 9th AF, & the US tactical air wings in the UK.
At this point I have to think the early Overlord 1.0 would have been expanded whoever commanded in 1944. Morgan was not wedded to the early plan, and understood what was required for a truly decisive invasion. It makes a bit more sense to ask the question of the original post as applying to 1943 rather than 1944.
A few other bits.
The Overlord 2.0 plan Monty unveiled in early 1944 was only of four beaches. The Brits were upped to two beacheads, but there were still not expected to be enough landing craft for more by the target date of 1 May. Utah Beach was added after map exercises showed Cherbourg could not be quickly captured with US 1st Army starting from OMAHA Beach only. Adding UTAH Beach meant a delay for delivery of additional landing craft. The rapid capture of Cherbourg was considered absolutely essential to the sucess of Overlord so Ike & the others bit their lip and accepted it. Ironically Cherbourg was captured far later than thought possible and proved less important than thought.
The targets for the several airborne divisions were changed multiple times between December and May. One early target for the Brits was somewhere south of Caen, the airfield? A US AB div was to be dropped on a unused airfield on the west side of the Coteinten penensula.
So, we can see that Monty (and others) rewrote his plan originally put to paper in Janauary.