Mussolini isn't really a hardcore fascist, more like a Salazar. He is somewhat of an evangelist, pandering to a largely catholic base with a number of social wedge issues.
Religious intolerance towards Muslims causes Italy's relations with Albania to sour, and as a result Albania seeks greater autonomy from Italy. The search for a new ally, along with the increased sense of religious identity/awareness, results in Turkey being this ally.
Turkey is similarly unfriendly with Italy due to the latter's attempts to carve up Turkish land in the Treaty of Sevres. If the opportunity comes up, Turkey would love to take back the Dodecanese Islands, and possibly even Libya, which was taken from them by Italy in 1912.
After anschluss, Germany thinks of demanding the ethnically German province of South Tyrol from Italy.
In 1937, Italy invades Ethiopia. They use poison gas and commit other war crimes as they did in OTL.
Germany publicly demands South Tyrol once Mussolini's troops have been mobilized to Ethiopia, and as per a secret treaty, Albania, Yugoslavia, and Turkey simultaneously propose a measure at the League of Nations conference announcing a coalition to enforce Article X of the League Covenant, with Ethiopia's permission. Ethiopia agrees and the motion carries, as nobody condones Italy's actions.
The Coalition declares a punitive war on Italy in defense of Ethiopia, and accepts Germany's request to join them. All of these countries has agreed in a secret Treaty how the territories will be divided.
- Eritrea and Somalia go to Ethiopia
- South Tyrol goes to Germany
- Fiume and other areas go to Yugoslavia
- Dodecanese and Libya returned to Turkey
- Sardinia is released as a Class A League Mandate
As a result, Ethiopia becomes more nationalistic, becoming a hero of blacks around the world.
Also, the League of nations has a much greater reputation than in OTL.
Germany declares the Ethiopians "Honorary Aryans"
This is a huge victory for the anti-colonial movement, emboldening leaders like Chandra Bose.
Ethiopia, with the support of Germany, sponsors all sorts of rebellions in French/British colonies in East Africa.
Turkey, with the support of Germany, sponsors similar movements in Egypt and the Levant.
Once WW2 starts, the Allies are completely spread thin, having to abandon much of their colonial possessions. They will likely have to settle for a negotiated peace of some sort.
Sorry and after Italy had finished to break every one of them what happen? Because this will happen.
Germany at the moment don't have an army or an air force and Anshluss happened in 1938 with Italian agreement due to the support (both economical and political during the invasion of Ethiopia), so not only what Germany have will attack a place that made a direct assault at the Maginot Line look like a party but also need to do get Austria earlier without Italy having any problem and hardcore fascist or not, Benny will have problem with that without a motive like OTL.
Turkey armed forces are not capable to attack Italy unless they have a strong desire of suicide, as they lack the mean, the equipment and the training.
Yugoslavia had almost have a civil war, a lot of unresolved internal problems and not really the most modern armed forces, doubt that they will do much against the fortified border.
Ethiopia at the moment is being beatean and at most hold the line, launching offensive is not really in her capacity...hell even before the war, except for raid she can't.
Frankly is like you launch an invasion of China by Birmania, Vietnam, Bhutan and Afganistan.