Engineering magnetic anisotropy in two-dimensional systems has enormous scientific and technological implications. The uniaxial anisotropy universally exhibited by two-dimensional magnets has only two stable spin directions, demanding 180° spin switching between states. We demonstrate a previously unobserved eightfold anisotropy in magnetic SrRuO₃ monolayers by inducing a spin reorientation in (SrRuO₃)₁/(SrTiO₃) _N superlattices, in which the magnetic easy axis of Ru spins is transformed from uniaxial 〈001〉 direction (N < 3) to eightfold 〈111〉 directions (N ≥ 3). This eightfold anisotropy enables 71° and 109° spin switching in SrRuO₃ monolayers, analogous to 71° and 109° polarization switching in ferroelectric BiFeO₃. First-principle calculations reveal that increasing the SrTiO₃ layer thickness induces an emergent correlation-driven orbital ordering, tuning spin-orbit interactions and reorienting the SrRuO₃ monolayer easy axis. Our work demonstrates that correlation effects can be exploited to substantially change spin-orbit interactions, stabilizing unprecedented properties in two-dimensional magnets and opening rich opportunities for low-power, multistate device applications.