Pod: the United Kingdom accepts the offer of alliance with the Ottoman Empire just prior to the great war. The ottoman Empire is propped up by the UK during the war, leading to a front opened in the Balkans even earlier in world war one. Food, ammunition, and other supplies is transported with little trouble into the black sea (ententea ottomans means no failed Gallipoli), keeping Russia in better shape, possibly even in the war.
1920s Is an era of prosperity for the Empire, which strengthens it's hold in Anatolia and the Arabian peninsula.
It plays an important part in the north African campaign during the alt ww2, supplying the allied powers with oil and aiding the Russian empire,which is headed by a reduced Tsar and the Russian duma (which whether or not the Russian Empire could or could not survive, but for simplicity let's say yes) during the siege of St. Petersburg.
1941 pearl harbor brings in the US of A to the party.
1945, Hitler's Germany is completely shattered into various states. Some people think the Jews need a homeland, especially the survivors. The ottoman Empire is not in the mood to let the Jewish people have Palestine, and is strong enough not to be pushed around. The historic Hanover is designated a Jewish homeland in 1948 and the other German States fall under either French, British, or Russian influence.