The establishment of the concept of sustainable, decentralised, multi-carrier energy systems, together with the declining costs of renewable energy technologies, has proposed changes in off-grid electrification interventions towards the development of integrated energy systems. Notwithstanding the potential benefits, the optimal capacity planning of such systems with multiple energy carriers—electricity, heating, cooling, hydrogen, biogas—is exceedingly complex due to the concurrent goals and interrelated constraints that must be relaxed. To this end, this paper puts forward an innovative new optimal capacity planning method for a first-of-its-kind stand-alone multiple energy carrier microgrid (MECM) serving the electricity, hot water, and transportation fuel demands of remote communities. The proposed off-grid MECM system is equipped with solar photovoltaic panels, wind turbines, a hydrogen-based energy storage system—including an electrolyser, a hydrogen reservoir, and a fuel cell—a hybrid super-capacitor/battery energy storage system, a hot water storage tank, a heat exchanger, an inline electric heater, a hydrogen refuelling station, and some power converters. The main objective of calculating the optimal size of the conceptualised isolated MECM’s components through minimising the associated lifetime costs is fulfilled by a specifically developed meta-heuristic-based solution algorithm subject to a set of operational and planning constraints. To evaluate the utility and effectiveness of the proposed method, as well as the technical feasibility and economic viability of the suggested grid-independent MECM layout, a numerical case study was carried out for Rakiura–Stewart Island, Aotearoa–New Zealand. Notably, the numeric simulation results highlight that the optimal solution presents a low-risk, high-yield investment opportunity, which is able to save the diesel-dependent community a significant 54% in electricity costs (including electrified space heating)—if financed as a community renewable energy project—apart from providing a cost-effective and resilient platform to serve the hot water and transportation fuel needs.