  We introduce a simple model of SO($N$) spins with two-site interactions which
is amenable to quantum Monte-Carlo studies without a sign problem on
non-bipartite lattices. We present numerical results for this model on the
two-dimensional triangular lattice where we find evidence for a spin nematic at
small $N$, a valence-bond solid (VBS) at large $N$ and a quantum spin liquid at
intermediate $N$. By the introduction of a sign-free four-site interaction we
uncover a rich phase diagram with evidence for both first-order and exotic
continuous phase transitions.
