We study theoretically the transverse spin associated with the eigenmodes of a thinmetal film embedded in a dielectric. We show that the transverse spin has a direct dependence on the nature and strength of the coupling leading to two distinct branches for the long- and short-range modes. We show that the short-range mode exhibits larger extraordinary spin because of its more ‘structured’ nature due to higher decay in propagation. In contrast to some of the earlier studies, calculations are performed retaining the full lossy character of the metal. In the limit of vanishing losses, we present analytical results for the extraordinary spin for both the coupled modes. The results can have direct implications for enhancing the elusive transverse spin exploiting the coupled plasmon structures.