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Abstract We propose to generate and control stationary one-way steering with strong entanglement between photon and magnon modes by the cooperative effect of coherent coupling and dissipative coupling. Due to the combination of two couplings, the system becomes a parity-time-like symmetric non-Hermitian system, and two exceptional points (EPs)-like appear in the real and imaginary parts of the eigenvalues. We demonstrate that the especially obvious quantum entanglement and perfect one-way steering can be obtained around two EPs-like. The continuous variable entanglement and steering produced by this cooperative effect show stronger robustness to environment temperature and system dissipation than that induced by nonlinearity. The one-way steering directivity can be controlled by the relative phase of cooperative dissipation and the frequency detuning of the magnon mode. Our work shows the controllability advantage of the open cavity magnonic system and may open up a platform for the generation of stationary one-way steering.