We report the first systematic measurement of x-ray emission anisotropies following dielectronic, trielectronic and quadroelectronic recombination into He-like through O-like iron and krypton ions. Using the experimental data we calculated the polarization of the Kα x rays in an anisotropic plasma as a function of the plasma temperature. Unexpectedly, we found that the degree of polarization is dominated by previously neglected trielectronic and quadroelectronic recombination resonances.