We first show that the effective nonrelativistic theory of gravitationally interacting, massive integer-spin fields (spin-0, 1, and 2 in particular) is described by a 2s+1 component Schrödinger-Poisson action, where s is the spin of the field. We then construct s+1 distinct, gravitationally supported solitons in this nonrelativistic theory from identically polarized plane waves. Such solitons are extremally polarized, with macroscopically large spin, but no orbital angular momentum. These s+1 solitons form a basis set, out of which partially polarized solitons can be constructed. All such solitons are ground states, have a spherically symmetric energy density but not field configurations. We discuss how solitons in higher-spin fields can be distinguished from scalar solitons, and potential gravitational and nongravitational probes of them.