Can my brokerage firm enter into a contract with another firm where we agree upon a cooperating split for all cooperative transactions involving our two companies?

No. Under the NAR settlement, it is the seller, not the listing broker, who decides whether or not there will be a cooperating split offered, and if so, the amount of the split. A listing firm should not enter into an agreement that purports to commit all of their future sellers. Moreover, regardless of any agreed upon split between the listing firm and the cooperating firm, the cooperating firm can receive no more than the amount agreed to by the particular buyer in their contract with the cooperating firm. In short, going forward, commissions paid to cooperating firms must be dealt with on a per transaction basis.