It would make an interesting ATL to see Mussolini playing a good diplomatic game for long-term gain. I don't see Mussolini having the skills needed. Is there a prominent Italian diplomat that can easily fill the role?
Bastianini, the then italian ambassador in the UK and his predecessor Dino Grandi were well know italian diplomat and were opposed at the italian Dow and will have supported such agreement and at least have more direct experience in foreign relations than Benny. The problem is Mussolini, with the fall of France he was really convinced that the war was basically over, you need him incapacitated (even temporary), getting prudent for still a little while or the King coming strong against the Dow.
I love this idea. The Italians negotiate a deal that is really not too far from OTL deal Hitler imposed anyway. The main difference is the Italians get Malta, Savoy, and Nice along with a colony to be named later. Are you thinking Tunisia or some British Colony?
You can then take this idea and do something like Calbears ATL or any other version of 'German goes East' that you like.
Nice and Savoy (or Corsica) IMVHO are a little too much, Adolf is still trying to bring Vichy onboard and make her cede national territory will greatly erode Petain legitimancy...Tunisia is more probable (but still need tough negotiation and it's hardly a given). Somaliland had the right combination of being showy and at the same time useless enough to be seriously considered; while Malta on the general military wisdom of the time, was considered already lost if the italian enter the conflict so giving her away was the lesser evil; more probable are enlargement of Libya at the expense of Tunisia, Chad,Algeria and Egypt maybe Cassala and other border adjustment in east africa.
The German advantage in having Italy neutral aka not wasting troops and material in Africa and Greece (Jugoslavia will probably be invaded in any case due to the internal political instability and the pro-british coup) while not war winning can worse a lot the Soviet situation (very important thing for the war aftermath) and even cause the fall of Moscow or a victory at Stalingrad. Naturallly much depend if Stalin in this scenario again convince himself that Adolf will not attack him for now.
On this deal, we still have issues of fear of the French Navy falling into German hands. Do you think the UK might support the Italians 'purchasing' some French battleships?
Probably, even if Regia Marina will be more interested in Cruiser, Destroyers and other support vessel; in any case there is the possibility that withtout Regia Marina in the picture, the British will be less scaried by a possible invasion and will leave the French Fleet alone, making De Gaulle job in recruiting for the Free French easier (and maybe avoiding Mers-el Kebir and Dakar)