In developing epithelia, the core planar polarity proteins physically interact with each other and localize asymmetrically at opposite cell ends, forming intercellular complexes that link the polarity of neighboring cells. Using quantitative imaging to examine the composition of the core protein complex in vivo, we find that complex composition is unexpectedly plastic. The transmembrane proteins Frizzled and Flamingo form a stoichiometric nucleus in the complex, while the relative levels of the other four core proteins can vary independently. Exploring the functional consequences of this, we show that robust cell polarization is achieved over a range of complex stoichiometries but is dependent on maintaining appropriate levels of the components Frizzled and Strabismus. We propose that the core proteins assemble into signalosome-like structures, where stable association is not dependent on one-to-one interactions with binding partners, and signaling functions can act over a wide range of complex compositions.