Although seawater is abundant, desalination is energy-intensive and expensive. Using the sun as an energy source is attractive for desalinating seawater; however, the performance of state-of-the-art passive devices is unsatisfactory when operated at less than one sun ($<$ $1$ $kW$ $m^{-2}$). Here, we present a completely passive, modular, and low-cost solar thermal distiller for seawater desalination. Each distillation stage is made of two opposed hydrophilic layers separated by a hydrophobic microporous membrane, and it does not require further mechanical ancillaries. Under realistic laboratory and outdoor conditions, we obtained a distillate flow rate of almost $3$ $L$ $m^{-2}$ $h^{-1}$ from seawater at less than one sun - twice the yield of recent passive device reported in the literature. In perspective, theoretical modelling suggests that the distiller has the potential to further doubling the peak flow rate observed in the current experiments. This layout can satisfy freshwater needs in isolated and impoverished communities, as well as realize self-sufficient floating installations or provide freshwater in emergency conditions.