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The correct statement asserts that a member firm may, but is not required to, accept stop orders. Broker-dealers have discretion in their operations, which includes the acceptance of different types of orders from clients. While it is common practice for many firms to accept stop orders, it is ultimately at each firm's discretion depending on their policies and the systems they have in place.

Stop orders are designed to be executed once the market price reaches a specified level, which can help investors manage potential losses or enter trades at desired price points. However, the regulatory framework does not mandate that firms must accept these orders, allowing them the flexibility to establish their own order acceptance policies.

In contrast, the other statements inaccurately assert requirements or prohibitions that do not reflect the operational autonomy allowed for broker-dealers in this context. For instance, imposing a requirement to accept stop or stop limit orders lacks foundation in the rules governing broker-dealers, as it underestimates their flexibility in choosing which orders to process. Understanding this distinction underscores the principle of operational discretion in securities trading.