President Barack Obama is under fire from all sides after his statement that the United States doesn't "have a strategy yet" for defeating the Islamic State (ISIS), but a military plan is evolving in Iraq all the same.

At first, when the president announced limited airstrikes, he stressed that the United States was taking action to support Iraqi ground forces while halting ISIS advances. But the air war is expanding, reports The Daily Beast. In addition, the United States is forming alliances with groups that have fought against American troops in the past, but who want ISIS defeated.

The initial reasons the strikes were ordered were to to protect American personnel in Erbil; to save the Yazidi minorities trapped on Mount Sinjar; to protect the Mosul Dam; and to break ISIS’s siege on the Shiite town of Amirli.

At first, the missions centered on humanitarian relief, dropping much-needed water and supplies to the Yazidis, and on defense maneuvers to protect Erbil.

But after a week, as ISIS started being pushed back, the mission started to shift, and the air strikes have become more offensive than defensive. United States aircraft is now bombing ISIS targets while supporting Kurds, the Iraqi military and once anti-American militia groups who are now fighting ISIS.

"The ground coalitions we’re supporting with air power are uniquely different in each case," Doug Ollivant, a former advisor to Gen. David Petraeus who served in the National Security Council under Presidents George W. Bush and Barack Obama, told The Daily Beast. "In Sinjar, it’s largely the PKK [a Kurdish militia] who rescued the Yazidis. In Mosul, it was the Golden Brigades [An elite unit of the Iraqi army] with the Peshmerga in support, and in Amirli it looks like Shia militias with the Iraqi military in support."

But the PKK, or the Kurdistan Workers' Party, is still considered a terrorist organization, and forming an alliance with its fighters could cause issues with U.S. relations with Turkey. The leftist organization has been fighting against the Turkish government for several years, but as its fighters have been fighting alongside Kurdish forces against ISIS in recent weeks, the PKK has become a vital part of the fight against ISIS.

Joining forces with the PKK, however, could add a psychological element to the battles.

Women fight with the PKK, and some told Stars and Stripes that they want to kill ISIS soldiers who have raped women and sold them into slavery across Iraq and Syria. Extremists such as those fighting with ISIS believe they will not enter heaven if they are killed in battle by a woman.

Another group, Asaib Ahl al-Ahq, is spearheading U.S. operations in Amirli. During the last war in Iraq, the group was known for sectarian violence against Sunnis and for its attacks on U.S. troops.

But while the group is backed by American airstrike power, that doesn't make it one of the United States' newest allies. A spokesman told The New York Times that the group doesn't trust Americans at all and "we don't need them."

Obama insists that the U.S. military can only be part of a political solution as agreements are made with such sectarian groups. He also insists Baghdad will need to reintegrate Sunnis who support ISIS. However, that could be difficult if the United States appears to back Shiite groups, warns University of Maryland researcher Phillip Smyth.

"If your goal is to cause some level of reconciliation, [Amirli] doesn’t assist it one bit,” said Smyth. "The fact is this is being promoted by Tehran as an Iranian initiative. It’s them saying we run the show.”

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