McLEAN, Va.—Top Central Intelligence Agency officials are pressing spies, analysts, scientists and even economists into new teams as they broaden their efforts against Islamic State militants and other global threats.

The reorganization is part of a broader effort by director John Brennan to break down CIA “stove pipes” that have been in place for decades, which some felt isolated the agency’s secretive spy network from its internal religious experts, computer hackers, linguists, and others.

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