The borders of the Islamic State‘s “caliphate” are shrinking fast. The group’s strongholds in Iraq and Syria are collapsing one by one. The U.S.-led war has reached a point where questions are being raised about what comes next.

So far, the answer seems likely to be: more war.

That’s partly because the U.S. strategy for defeating the Islamic State relies on a variety of regional allies and local armed groups who are often bitterly at odds. Though all of them regard the Islamic State as an enemy, most of them regard one another as enemies, too. As they conquer territory from the militants, they are staking out claims to the captured lands in ways that risk bringing them into conflict with others who are also seizing territory. New wars are brewing, for control of the post-Islamic State order.

Here is a list of 10 of them, in no particular order. There are doubtless more. Some have already started. Others may never happen. But any one of them could increase the Islamic State’s chances of survival, perpetuating the conditions that enabled the group to thrive — and perhaps entangling the United States in the region for many years to come.

WAR NO. 1: U.S.-backed Syrian Kurdish forces and Turkish-backed Arab forces

This is one of the wars that have already started, and it is also one of the more complicated ones. Turkey, which is fighting a war at home against separatist Turkish Kurds, has watched with alarm as Syrian Kurds have capitalized on U.S. support to expand Kurdish control over northeastern Syria. Syrian Arab rebels allied to Turkey are also opposed to the Kurdish expansion, which is encroaching on Arab areas. So when Turkey intervened in Syria two weeks ago to help Syrian rebels capture Islamic State territory, it was clear that the Kurds were as much of a target as the Islamic State. Fighting has since erupted, and though the United States has asked both sides to stop, it is unclear whether the it has enough leverage over its rival allies to prevent a deepening conflict.

WAR NO. 2: Turkey and the Syrian Kurds

This war would be similar to war No. 1, but bigger. For now, Turkey has confined its incursion into Syria to an area of Syria occupied by the Islamic State that is mostly Arab. But Turkey is just as worried about the de facto Kurdish state emerging along its border farther east. Kurds declared an autonomous region there earlier this year, and Turkey is now building a wall along the border to try to seal it off. If the tensions persist, a direct Turkish invasion of the Kurdish area — where a small number of U.S. troops also are based — can’t be ruled out.