N.H. Rev. Stat. Ann. § 546-B:10

In responding to registrations or petitions for enforcement of 2 or more child support orders in effect at the same time with regard to the same obligor and different individual obligees, at least one of which was issued by a tribunal of another state or a foreign country, a tribunal of this state shall enforce those orders in the same manner as if the orders had been issued by a tribunal of this state.