With the United States on the verge, once again, of military action in the Middle East, it’s important to look at the Syrian conflict as what it is: the epicenter of a widening regional conflict. The limited U.S. missile strikes expected to punish the regime of Bashar al-Assad for the use of chemical weapons will sink the United States more deeply than ever into this turbulent quagmire. But there’s no guarantee that inaction would help the Obama administration get out or stay out. The regional players include too many American allies that are too important to U.S. interests, even though many of them are rivals and enemies of each other.

Let’s start with the Saudis, not least because Washington and Riyadh have had such close ties for so long, especially in the dark world of covert operations.

Saudi Prince Bandar bin Sultan used to be one of the most popular figures in Washington, D.C., where he was ambassador, and for that matter in Aspen, Colorado, where he owned an enormous mansion. With a cigar in one hand and a snifter of cognac in the other, he helped guide successive American administrations through the maze of intrigues in the Middle East, and helped create quite a few of them himself, including the arming of the Afghan mujahedeen and the complicated conspiracy that came to be known as Iran-contra.

Since Bandar’s 22-year tenure in Washington came to an end in 2005, he has moved deeply into the shadows, and is now the head of his country’s intelligence services.

The Saudis see Iran as the single greatest threat to their security militarily (especially if it gets nuclear weapons), religiously (Shiite versus Sunni), and even territorially (by promoting unrest among the Shiite populations of Saudi Arabia’s Eastern Province and in neighboring Bahrain). And in many respects the Syrian war is a proxy war between Saudi Arabia and Iran, but, of course, it’s not as simple as that.

The Syrian regime of Bashar al-Assad and his father, Hafez al-Assad, before him have been intimate allies of the Iranian mullahs since the 1980s. Together, Iran and Syria have trained and armed Lebanon’s Hezbollah, one of the most effective guerrilla and terrorist organizations in the world.

In 2006, Prince Bandar actually encouraged Israel to wage what turned out to be a failed effort to obliterate the Hezbollah militia in Lebanon. Saudi support for Sunni rebels in Iraq also is meant to undermine a government in Baghdad that has grown ever closer to Tehran. Today, the Saudis have every interest in using the Syrian conflict to weaken Iran by depriving it of its allies in Damascus, or, at a minimum, draining Iran’s resources in a protracted Syrian war.

But there’s a twist. A secondary but significant Saudi concern is the Muslim Brotherhood, an international organization of Sunni Islamists that has deep roots in Syria and a clear ambition to dominate its political future. While the Saudis and the Brotherhood share the goal of deposing Assad, they are bitter enemies. For years the royal House of Saud has worried that the holier-than-thou Brotherhood could threaten its own intertwined religious and political legitimacy.

When the Brotherhood emerged as the most potent political force in the region by exploiting the supposed democratization that followed the toppling of familiar dictators in 2011, the Saudis worked to undermine the organization wherever they could. This summer they have given massive financial backing to the regime of Egyptian Gen. Abdel Fatah al-Sisi, who ousted elected Egyptian President Mohamed Morsi and who is determined to exterminate the Brotherhood’s organization even if it means killing thousands of people.

On the Syrian battlefield, the lines between the Brotherhood and Jabhat al-Nusra, an offshoot of al Qaeda, often are blurred. The Saudis do not want to support either organization as such. But Riyadh is very concerned that the governments of Turkey and of Qatar, both of which have close ties to the Brotherhood, will dominate the Syrian scene if the Saudis themselves do not take the lead by supplying covert funding and arms to try to buy influence and control. It’s a tricky game, but of a kind that the Saudis have played for generations.

The other great American ally in the region, Israel, has for the most part recused itself from the Syrian conflict. Its only direct action has been to strike Hezbollah supply networks that might have carried threatening missiles into Lebanon, and to shell Syrian fighters who brought their war too close to the Israeli frontier. In fact, although Saudi Arabia and Israel are technically enemies, their interests coincide very closely in Syria. Both want to see Iran weakened, neither wants to see Assad last, and neither want to see the Brotherhood or al Qaeda take control. In such a situation, a protracted war draining the resources of its enemies is not the worst thing that could happen from Israel’s point of view.

Last but not least among the regional players there is the little kingdom of Jordan, where the intelligence services have very close and longstanding ties to the Saudis, the Israelis, and the Americans. Jordan’s King Abdullah has denied repeatedly that his country is being used as a staging area for the CIA to train Syrian guerrillas. But there have been several reports that such units crossed from Jordan into southern Syria in recent weeks.

A limited American-led attack on Syria will do nothing to sort out these complicated alliances and conflicting enmities. At best, Assad might be persuaded not to use chemical weapons again. But Syria, almost certainly, will continue to bleed for years to come.