The U.S. and the U.K. are exploring ways to step up their campaign against Houthi militants in Yemen without provoking a broader war, with a focus on targeting Iranian resupplies and launching more aggressive pre-emptive strikes, people familiar with the matter said.

The proposals could mark an escalation in the allied effort to end the chaos in the Red Sea, which handled about 12% of global trade before the Houthis began targeting commercial ships in response to Israel’s bombardment of the Gaza Strip. The Houthi attacks have led to higher insurance costs and provoked fears of fresh inflationary pressure as ships take a longer and costlier route around the southern tip of Africa.

The risk is that more aggressive action will put the U.S. in direct conflict with Iran and provoke the sort of regional conflagration that President Joe Biden says he wants to avoid.