ERBB2 and cancer: •Different valencies of the BsAbs did not significantly impact their effectiveness in fighting tumors•Fc domain enhanced the BsAbs’ ability to induce cytotoxic activity against the cancer cells•The Fc domain also triggered T-cell activation in a manner unrelated to the presence of the target antigen•The BsAbs efficiently redirected T cells to effectively eliminate all cancer cells expressing HER2 including those with low levels of HER2 expression