Sliding ferroelectricity (SFE) found in two-dimensional (2D) van der Waals (vdW) materials, such as BN and transition-metal dichalcogenides bilayers, open an avenue for 2D ferroelectric materials. The multiferroic coupling in 2D SFE materials is expected to bring about new concepts for spintronic memory devices. Here, using first-principles calculations, we demonstrate that the recently-synthesized MnSe multilayers [ACS Nano 15, 13794 (2021)] have large reversible out-of-plane electric polarization (~10.6 pC/m) and moderate interlayer sliding barriers superior to the existing 2D SFE materials. More interestingly, the intrinsic electric polarization is also accompanied by nonzero net magnetic moments whose direction is dependent on the electric polarization direction and thus can be switched by interlayer sliding. Additionally, both the SFE and magnetoelectric coupling can be effectively regulated by external strain and/or hole doping. Our findings suggest the potential of MnSe multilayers in 2D multiferroic and spintronic applications.