Systems and processes for purifying and concentrating a liquid feed stream are disclosed. In the systems, the concentrated liquid output from the high pressure side of a reverse osmosis stage is used as the draw solution in the low pressure side of the reverse osmosis stage in a configuration called osmotically assisted reverse osmosis. This reduces the osmotic pressure differential across the membrane, permitting high solute concentrations to be obtained, hastening the purification of the liquid. Reduced system pressures are also obtained by arranging multiple osmotically assisted reverse osmosis stages in a cross-current arrangement. Overall system energy consumption is reduced compared to conventional thermal processes for high concentration streams.