The IRS defines withholding agent very broadly. Every U.S. or foreign person who controls, holds custody of, receives, disposes of, or pays any item of income to a foreign person that is subject to NRA withholding is a withholding agent.
A withholding agent includes (without limitation) individuals, corporations, partnerships, trusts, associations or any other entity including individuals or entities acting as agents or intermediaries.
Your organization is a withholding agent even if there are other organizations or individuals who meet the definition of withholding agent as to an income payment. If more than one person is a withholding agent as to a single payment, the total withholding should not exceed 30 percent. When there are several withholding agents with regard to a single payment, they all have joint and severable liability.