  We devise a cold-atom approach to realizing a broad range of bi-linear
quantum magnets. Our scheme is based on off-resonant single-photon excitation
of Rydberg $P$-states (Rydberg-dressing), whose strong interactions are shown
to yield controllable XYZ-interactions between effective spins, represented by
different atomic ground states. The distinctive features of F\"orster-resonant
Rydberg atom interactions are exploited to enhance the effectiveness of
Rydberg-dressing and, thereby, yield large spin-interactions that greatly
exceed corresponding decoherence rates. We illustrate the concept on a spin-1
chain implemented with cold Rubidium atoms, and demonstrate that this permits
the dynamical preparation of topological magnetic phases. Generally, the
described approach provides a viable route to exploring quantum magnetism with
dynamically tuneable (an)isotropic interactions as well as variable space- and
spin-dimensions in cold-atom experiments.
