Even in the midst of ongoing attacks such as the ones that targeted hospital facilities in Aleppo, Russia and the U.S. have at least agreed on a plan for a cessation of hostilities. Here are two important examples. In December 2015, the United States and Russia agreed on U.N. Security Council Resolution 2254. The resolution’s road map for peace led to the current Geneva negotiations, which have been temporarily suspended. And before that, in 2013, the two countries agreed to eliminate Syrian chemical weapons, implemented in 2014.

Given this, we argue that the United States and Russia can work side by side, if not together, to defeat the Islamic State in Syria. If successful, they could push their respective Syrian allies into negotiations toward a multi-ethnic, multi-sectarian, unified Syria. While their goals are not completely aligned, we believe that each side’s positions are flexible enough to make at least some compromise possible.

On the one hand, the United States and Russia disagree about whether Assad should stay in power. On the other, the Islamic State may be enough of a threat to push this pair of frenemies into working together.

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What do the U.S. and Russia agree on?

Both the United States and Russia urgently want to defeat the Islamic State. That’s the only reason the United States intervened directly in Syria at all. The United States also wants to defeat or at least weaken other Islamist extremists among the anti-Assad rebels, particularly al-Nusra, the al-Qaeda affiliate in Syria. So do the Russians.

What else do the United States and Russia agree on? Well, both want Syria to remain one unified country rather than being broken up into sectarian bits. That might be hard to picture now, considering how bitterly divided the country is. While the country may end up with some kind of federal system, both the United States and Russia would prefer to avoid partition.

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Where do the U.S. and Russia disagree?

First, should Assad stay or go? That’s the biggest disagreement between Russia and the United States.

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Russia wants Assad in place to hold back Islamist radicalization. Airstrikes alone can’t defeat the Islamic State — but no outside powers are ready to put their own soldiers on the ground. The Russians believe that the best option is an alliance with the Syrian army and the nation’s sectarian militias.

That’s because Russia says that fighting both Assad and ISIS at the same time, as the United States wants, will not only fail but will lead directly to a genuine Islamic State, with Damascus as its capital. After all, getting rid of Moammar Qaddafi left Libya in chaos that has spread across the region.

But the United States wants Assad to go. The United States and its European allies blame the Syrian president for turning a domestic protest into a civil war. They believe Syria won’t have peace so long as Assad stays in power.

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Second, Russia and the United States disagree on how exactly to approach the various opposition groups. Russia tends to ignore the distinction between the Islamic State and other groups, viewing ISIS as but one group of jihadi fighters, which could mutate into some other similar group. For Russia, any opponent of Assad is a force for instability to be opposed.

The United States, in contrast, draws sharper distinctions between Syrian opposition groups, arguing that some are “moderate” and deserve support.

Third, Russia and the United States would each like to maintain or increase their influence in the region, and limit each other’s role. Russia wants to be able to shape the future of the region to suit its interests. The Russian leadership has no doubt that the Middle East will be an area of severe instability for years — if not decades — to come. Since this instability will inevitably spill over to Eurasia, Moscow wants a presence there to project power and to influence political developments.

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Since refugees have begun flooding into Europe, it’s become clear that European security is linked to Middle East stability. Russia believes that controlling Syria is key to controlling the security situation and future of the region.

At the same time, of course, the United States has long sought to be the dominant power in the region and finds Russian intervention irksome.

So can there be compromise?

Yes. Consider the question of Assad. The United States and European Union alliance have recently softened, suggesting that Assad may stay in power for some undefined ‘“transitional” period. Who knows how long that might last?

Moscow has also indicated that it is not bound to support the Assad family forever. However, the Russians say they believe a new power structure can be discussed only after the territory of Syria (ideally whole, possibly divided) is secured and the Syrian state survives.

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The United States and Russia are unlikely to have a meeting of the minds about the “moderates” that the United States supports and Russia bombs. However, the two powers have already agreed on a peace process designed to bring many of these groups to the bargaining table. The main sticking point in that regard has been with the parties themselves, rather than the United States and Russia. So while the two nations will not support the same groups, they do support negotiations among these groups, which offers some hope of an eventual cease-fire.

The larger geopolitical pushing and shoving seems like a luxury that neither side can afford for long. With oil prices this low, Russia will find a long-term military commitment draining. The United States, for its part, has shown little appetite for another land war in the Middle East, so a compromise solution is the best possible outcome for both parties.

What might cooperation look like?

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So what should we expect to happen next? The United States and Russia are brokering peace negotiations with the aim of ending the war and preserving Syria as a multi-ethnic, multi-sectarian state. With this in mind, the parties are trying to gain as much territory on the ground as they can before the cease-fire.

If neither side can secure a military victory, they will eventually have to turn to negotiations. The path will be enormously difficult. But if each group needs outsider supporters like the United States and Russia — and they would — then those two would have considerable leverage.

Of course, there’s a danger that other issues — like Ukraine — could get in the way of U.S.-Russian cooperation. But if the two powers stay focused, together they could help end the Syrian war.