<p>In Kaluza-Klein compactifications, some symmetries of the higher dimensional theory are preserved in lower dimensions, others are broken, and occasionally, there are symmetry enhancements. The symmetries that are enhanced by toroidal compactifications were recently shown to define a symmetry principle with constrained parameters that fixes the action <i>before</i> dimensional reduction. Here we show the opposite: symmetries of the higher dimensional theory that are broken in the reduction process, can actually be realized <i>after</i> dimensional reduction as a global symmetry principle with constrained parameters that fixes couplings in the lower dimensional theory. We implement this principle in pure gravity, half-maximal supergravity and the circle reduction of 11 dimensional supergravity to Type IIA superstring theory. As a further application, we show that it can be used to constrain the quartic Ramond-Ramond couplings in Type IIA superstring theory from the four-point <i>ζ</i>(3) <i>α</i>′³ <i>t</i>₈<i>t</i>₈<i>R</i>^{(<i>−</i>)4} interactions.</p>