Astrophysical neutrinos at EeV energies promise to be an interesting source for astrophysics and particle physics. Detecting the predicted cosmogenic (Greisen-Zatsepin- Kusmin, "GZK") neutrinos at 1016 - 1020 eV would test models of cosmic ray production at these energies and probe particle physics at ∼100 TeV center-of-mass energy. IceCube may be able to detect ∼10 GZK events per year with an extension including optical, radio, and acoustic receivers sparsely arrayed surrounding the optical core. Such a detector would feature crosscalibration with coincident events and would allow superior background rejection capability, energy and direction resolution, and confidence in discovered signals compared to single-method detectors. We present estimates of the neutrino effective volume for such a hybrid array both with the single-method sub-arrays independently and requiring combinations of sub-arrays to detect the same events. We also present ideas on hybrid event reconstruction and results from a proof-of-principle Monte Carlo test of a hybrid reconstruction algorithm.