In an announcement that could complicate the cornerstone of America’s mission in Iraq—training Iraq’s military to fight ISIS—an Iranian general said Monday that he also is prepared to begin training Iraqi military officers. The message comes after Baghdad and Tehran reached a security agreement in December, which has not been made public but will reportedly increase military cooperation between the two countries.

Washington and Tehran have quietly cooperated in the fight against ISIS largely by avoiding direct contact and keeping to separate spheres of influence. If Iran begins training Iraqi officers at the same time the U.S. carries out its own multi-year training mission, those spheres could collide. Iran hasn’t actually begun any training yet, only signaled its readiness, but if it does start, there are some obvious logistical questions to sort out that carry broader implications. It’s not clear whether the U.S. and Iran would split up the Iraqi army in some sort of shared custody training different units, or if a single Iraqi officer could end up receiving direction from both American and Iranian advisers.

The American military began training Iraq’s forces in late December, days before Iran and Iraq concluded their security agreement. Currently the U.S. vets Iraqi troops to ensure they don’t have ties to terrorist groups, but has not reported screening for ties to other armies.