Okay, here's a bit of a crazy one:
After 9/11, the Bush administration strikes a deal with Rauf Denktas, President of the Turkish Republic of North Cyprus: as an exchange for massive financial and political support, North Cyprus rents out the abandoned former luxury hotel area of
Varosha, Famagusta. Initially only used as an outpost for intelligence, the area is soon expanded into a military base, becoming a major strategic outpost for the US Army in the Iraq War, as well as monitoring Iran.
Unification talks between North Cyprus and the Republic of Cyprus fizzle out and tensions begin to rise between both sides, with rumours emerging that Turkey and the USA are moving more and more army personel into North Cyprus in order to rig the referendum in their favour. EU membership for Cyprus is put on hold. At the same time, American companies are getting interested in the former luxury sites of Varosha, buying them and turning them into prime real estate as well as luxury hotels. The same companies are also buying properties in the whole of Famagusta and the surrounding area, boosting the North Cypriot economy in order to get more popular support. The Annan plan referendum is delayed, tensions between both sides become increasingly hostile, with Greek far-right groups and EOKA veterans building up Greek Cypriot armed militias, and the US handing out Green Cards to Turkish Cypriots who work in Varosha, which increasingly becomes a de facto state within a state.
The year 2008 becomes a pivotal turning point, with three major events. The financial crisis leads to the emergence of the far-right Greek party Golden Dawn, which now also gets involved in Cyprus. Around the same time, the closure case against the AKP is successful and leads to political chaos, with Turkish Chief of Staff Mehmet Büyükanit temporarily taking over as head of government. The EU and the US don't recognise the new military leadership, but North Cyprus becomes a stronghold of the coup leaders, while Turkey descends into civil war. In the USA, John McCain becomes the new US President (defeating John Edwards), with Secretary of State Richard Armitage and National Security Advisor Kori Schake stressing the importance of a permanent US presence in Famagusta. The situation in Cyprus becomes increasingly gung-ho, with pro-Büyükanit forces dominating North Cypriot politics, and pro-Erdogan rebel groups (secretly backed both by the Republic of Cyprus and Greece) occassionally carrying out terrorist plots in the northern Nikosia area. Civil war emerges in Turkey, slipping over into North Cyprus, which also leads to the involvement of far-right Greek "volunteer groups", as the government of the Republic of Cyprus fear aggression by Neo-Kemalists in the Turkish army. Those skirmishes turn into full-scale civil war after 2012, when Russia decides to throw its military weight behind South Cyprus, sending in mercenaries.
The USA, being too much involved in Syria, Libya and Iraq to get involved in the Cypriot civil war, still maintains its presence in Varosha, which is now increasingly seen as a "safe haven" for refugees from both parts of the island. McCain wants a "stable and democratic Turkey" and therefore decides to support Erdogan, while acting against Büyükanit's forces in North Cyprus, as his government is not seen as legitimate. By this stage, the Turkish army has overrun most of the island, therefore American troops are now getting active and occupy the whole of Cyprus. The military administration issues a memorandum, banning all Greek, Russian and Turkish involvement on the island for ten years in order to prevent inter-ethnic tensions. More and more Cypriots now begin to regard the USA as a more neutral power than Turkey or Greece, and therefore happily agree to a long-term US presence, also boosed by the "Varosha effect": While the economy of Cyprus has being going downhill ever since 2008, due to the financial crisis and the civil war, the American enclave of Varosha was booming and is now being regarded as the future model for Cyprus. Several civic groups now push for statehood, which is now also advocated by the US government.