A stateful packet processing system includes: a first stateful stage including a first state table and a first finite state machine (“FSM”) table; and a second stateful stage including a second state table and a second FSM table. The system performs a distribution operation defining when a flow is processed by the first and/or the second stateful stage. The first and/or second FSM table is extended with states and transitions that support the distribution operation. The first and/or second stateful stage executes an evaluation operation that executes the distribution operation. The evaluation operation provides a criterion for moving a particular flow from one of the first or second stateful stage to the other stateful stage. The first and second stateful stages are included in a software-defined networking (“SDN”) switch. The distribution operation operates within defined capabilities of a software and/or hardware pipeline of the SDN switch.