A bin lift arrangement comprising platform for transporting storage containers between a plurality of vertically arranged storage grids (104/104') in a multi-level storage system, the grids of the storage system being vertically arranged with respect to each other, each grid of the multi-level storage system being of the type comprising a plurality of upright members and horizontal members defining a framework structure in the form of a grid section (104/104') of storage columns containing storage containers arranged in stacks, and having automated container handling vehicles (201/301) operating on a rail system (108/108') on a top level of the grid section (104/104'), the rail system comprising perpendicular horizontal tracks (110/111) upon which the vehicles can travel in a first direction and a second direction perpendicular to the first direction, the intersection of the perpendicular tracks further defining cells above grid columns, wherein the bin lift arrangement further comprises one or more vertical rails arranged outside and functionally adjacent to vertically aligned faces (400/400') of the grid sections (104/104'), wherein the platform is vertically movable along the one or more vertical rails arranged outside and functionally adjacent to vertically aligned faces (400/400') of the grid sections (104/104'), wherein the platform is horizontally adjustable in relation to the one or more vertical rails in an amount sufficient to accommodate a horizontal misalignment between the rail systems (108/108') of the respective grid sections (104/104'), and wherein the platform comprises a vertically movable frame member to which is connected a horizontally movable carriage member, the carriage member arranged for receiving containers, the carriage member being connected to the frame member by one or more guide wheels arranged to roll along one or more horizontal guide rails of the frame member, the carriage member further comprising one or more alignment wheels connected to the carriage at a position relative to vertical rails, whereby the guide wheels are arranged to, during vertical movement of the frame member, contact and roll up a sloped surface of a protruding alignment bracket mounted on the vertical rail, thereby causing the carriage member to move in the horizontal direction in relation to the frame member. the platform is vertically movable along the one or more vertical rails arranged outside and functionally adjacent to vertically aligned faces (400/400') of the grid sections (104/104'), wherein the platform is horizontally adjustable in relation to the one or more vertical rails in an amount sufficient to accommodate a horizontal misalignment between the rail systems (108/108') of the respective grid sections (104/104'), and wherein the platform comprises a vertically movable frame member to which is connected a horizontally movable carriage member, the carriage member arranged for receiving containers, the carriage member being connected to the frame member by one or more guide wheels arranged to roll along one or more horizontal guide rails of the frame member, the carriage member further comprising one or more alignment wheels connected to the carriage at a position relative to vertical rails, whereby the guide wheels are arranged to, during vertical movement of the frame member, contact and roll up a sloped surface of a protruding alignment bracket mounted on the vertical rail, thereby causing the carriage member to move in the horizontal direction in relation to the frame member.