for each regular coadjoint orbit of a compact group, we construct an exhaustion by symplectic embeddings of toric domains. as a by-product we arrive at a conjectured formula for the gromov width of coadjoint orbits. our method combines ideas from poisson-lie groups and from the geometric crystals of berenstein-kazhdan. we also prove similar results for multiplicity-free spaces. this is joint work with a. alekseev, j. lane, and y. li.