Most research on flexible job shop scheduling assumes constant processing speeds. However, in real production, machines need to operate at variable speeds to achieve energy-efficient scheduling, which requires balancing multiobjective between production efficiency and green development. Such tradeoffs thus trigger the phenomenon in which massive solutions converge to identical objective values (i.e., the multimodal property), which is often neglected in scheduling problems. To address the above challenges, this work introduces a knowledge-enhanced evolutionary multitasking memetic algorithm (KEMMA) to solve the multimodal multiobjective flexible job shop scheduling problem considering speed (MMFJSP-S). First, self-paced learning motivated us to construct a simple auxiliary task and employ an evolutionary multitasking (EMT) framework to tackle the complex MMFJSP-S. Moreover, a knowledge enhancement and explicit transfer strategy is designed to reduce the effects of negative transfer by reinforcing and sharing beneficial knowledge across tasks. Finally, a mapping transformation mechanism is proposed to handle the multimodal property of the MMFJSP-S in the decision space. By comparing with ten advanced algorithms, the experimental results verify the remarkable superiority of the proposed KEMMA in solving MMFJSP-S and reveal the significance of studying the multimodal property.