We propose an efficient scheme to realize almost perfect higher-order squeezing of two YIG spheres via microwave-mediated magnon–atom interactions. It is assumed that two microwave cavity modes are coupled to two YIG spheres by the magnetic dipole interaction and a superconducting artificial atom by the electric dipole interaction, respectively. When the microwave cavity fields are tuned to be far detuned from the dressed atomic Rabi sidebands and the magnon frequencies, the coherent coupling between two magnons and the artificial atom can be ...