As opposed to purely molecular systems where electron dynamics proceed only through intramolecular processes, weakly-bound complexes like helium droplets offer an environment where local excitations can interact with neighboring embedded molecules leading to new intermolecular relaxation mechanisms. Here, we report on a new decay mechanism leading to the double ionization of alkali dimers attached to helium droplets by intermolecular energy transfer. From the electron spectra, the process is similar to the well-known shakeoff mechanism observed in double Auger decay and single photon double ionization [1,2], however, in this case, the process is dominant, occurring with efficiencies equal to, or greater than, single ionization by energy transfer. Although an alkali dimer attached to a helium droplet is a model case, the decay mechanism is relevant for any system where the excitation energy of one constituent exceeds the double ionization potential of another neighboring molecule. The process is, in particular, relevant for biological systems, where radicals and slow electrons are known to cause radiation damage [3].