We design and demonstrate new types of optical tweezers with lateral pulling forces that allow full control of biological samples with complex geometric shapes. With appropriate beam shaping, the dual tug-of-war tweezers effectively hold and stretch elongated biological objects of different sizes, and the triangular tug-of-war tweezers with threefold rotational symmetry steadily hold asymmetric objects in the plane of observation and exert stretching forces along three directions. We successfully apply these tweezers to manipulate microparticles and bacterial cells in aqueous media.