The uptake of electric vehicles (EVs) is expected to trigger investments to adapt existing distribution networks, particularly in the low voltage (LV). To make adequate, holistic planning decisions over multiple years, the assessment of alternatives-such as reinforcements or the adoption of EV management strategies-must not only capture when the investments are needed but also the effects on customers and carbon emissions, all while accounting for uncertainties. This paper proposes a stochastic, practical, and scalable progressive multi-year planning methodology that considers technical, customer, economic and environmental aspects to make holistic planning decisions for existing LV networks to accommodate EVs. The proposed rule-based methodology contrasts the net present value and benefits of four planning alternatives: network reinforcements, EV charging point management, and their combinations. Uncertainties are catered for by adopting a Monte Carlo approach. Using two real UK LV networks and realistic time-series data, results demonstrate the importance of a holistic decision-making approach. From an economic perspective, EV management is better for voltage issues, and reinforcements for thermal problems. However, when customer effects are considered, the management can lead to unacceptable charging delays. Combinations, on the other hand, provide trade-offs between cost and the effects on customers or carbon emissions. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.