A search for Beyond the Standard Model double-β decay modes of ⁷⁶Ge has been performed with data collected during the Phase II of the GERmanium Detector Array (Gerda) experiment, located at the Laboratori Nazionali del Gran Sasso of INFN (Italy). Improved limits on the decays involving Majorons have been obtained, compared to previous experiments with ⁷⁶Ge, with half-life values on the order of 10²³ yr. For the first time with ⁷⁶Ge, limits on Lorentz invariance violation effects in double-β decay have been obtained. The isotropic coefficient å⁽³⁾ _of , which embeds Lorentz violation in double-β decay, has been constrained at the order of 10^-6 GeV. We also set the first experimental limits on the search for light exotic fermions in double-β decay, including sterile neutrinos.