A liquid handling system has a robot manipulator for orienting pipette or dispenser tips in relation to sample containers situated in or on the system, pipette or dispenser tips, drives for moving the robot manipulator, and processors for controlling the movements and actions of the robot manipulator and/or of the pipette or dispenser tips. The system also includes at least two blocks situated on two arms of the robot manipulator, at least two of the pipette or dispenser tips being situated on each block and at an axial distance to one another. The axial distance essentially corresponds to the grid spacing of wells of a microplate. At least one of these blocks, for the alternating interlaced orientation of the pipette or dispenser tips of at least two blocks along a shared line, are individually movable at least in the X direction. A method allows the time-saving pipetting over of liquid samples between diverse sample containers, e.g., between sample tubes and microplates having 24, 96, 384, or 1536 wells.