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Were that many divisions, and the shipping needed to support them, available in the ETO in September 1943?
On the US side there were eight divisions: 1st Arm, 2d Arm, 1st Inf, 3d Inf, 9th Inf, 34th Inf, 45th Inf, 82 Abn. Two Corps HQ the I Armored, and the II were sent. The I Armored was dissolved during 1943. Two Army HQ were stood up; the 5th and 7th. Both were never at full strength at the same time. While the 7th operated in Sicily the 5th served as a planning and preparations group for follow on operations in Italy. After the 5th Army became operational the 7th became a planning cell, preparing for Op ANVIL among other things. A third corps HQ was stood up in the autumn of 1943.
The Brits had two Army HQ at the start of 1943 1st & 8th. There was probably another in the Levant or Egypt responsible for the garrison units there. If I recall correctly there were five corps HQ split between 1st & 8th Armies. My list of Brit divisions in incomplete. 4thInf. 5th Inf, 46th Inf, 56th Inf, 78th Inf, 1st Arm, 6th Arm, 7th Arm, 10th Arm in Palestine, 1st Airborne, 1st Canadian Inf, 4th Indian, 2d New Zealand... and probably something I'd missed in Egypt or Palestine.
France had manpower mobilized for a dozen odd divisions in the Med, tho their equipment was falling apart and was obsolescent. In 1943 they committed a 'corps' to securing Sardinia and Corsica, and at the end of the year to Italy. The Poles had a division stood up in the Med in late 1943 & another in 1944.
So thats 20+ divisions fir for combat, six or seven corps HQ, 3-4 Army HQ.
I may be wrong but recall about 6,000 operational Allied aircraft in the Med in middle 1943.
Cargo ships are the trick. OTL operations in italy were hampered from October 1943 through 1944 by the priority to the OVERLORD operation and the related BOLERO build up. Then there was the 1943 commitment by the US to send equipment for some ten French infantry and armored divisions by US TO/TE. After that the liberated population of Italy proved dependent on Allied cargo ships to prevent starvation. After Op AVALANCHE in September the Amphi fleet began drawing down to prepare for Op NEPTUNE in the UK.