An antibody-like binding protein that binds to CD3 and to at least one further target antigen which is CD123, comprising two polypeptide chains that form two antigen-binding sites, wherein a first polypeptide has a structure represented by the formula [I]: V D1 -L 1 -V D2 -L 2 -C L [I] and a second polypeptide has a structure represented by the formula [II]: V D3 -L 3 -V D4 -L 4 -C H1 [II] wherein: V D1 is a variable domain of heavy or light chain of a first immunoglobulin; V D2 is a variable domain of heavy or light chain of a second immunoglobulin; V D3 is a variable domain of heavy or light chain of said second immunoglobulin; V D4 is a variable domain of heavy or light chain of said first immunoglobulin; C L is a light chain constant domain of an immunoglobulin; C H1 is a C H1 heavy chain constant domain of an immunoglobulin; L 1 , L 2 , L 3 , and L 4 are amino acid linkers; and wherein the first and the second polypeptide form a cross-over light chain-heavy chain pair, and wherein V D1 and V D2 are both either variable domains of light chains, or variable domains of heavy chains, and V D3 and V D4 are both variable domains of heavy chains if V D1 and V D2 are variable domains of light chains, or V D3 and V D4 are both variable domains of light chains if V D1 and V D2 are variable domains of heavy chains; wherein said first or second immunoglobulin is an anti-CD3 antibody which comprises a heavy chain variable domain comprising CDR1-H of sequence SEQ ID NO: 6, CDR2-H of sequence SEQ ID NO: 7, and CDR3-H of sequence SEQ ID NO: 8, and a light chain variable domain comprising CDR1-L of sequence SEQ ID NO: 142, CDR2-L of sequence 'KVS', and CDR3-L of sequence SEQ ID NO: 11; and wherein the other of said first or second immunoglobulin is an anti-CD123 antibody which comprises a heavy chain variable domain comprising CDR1-H of sequence SEQ ID NO: 381, CDR2-H of sequence SEQ ID NO: 384, and CDR3-H of sequence SEQ ID NO: 382, and a light chain variable domain comprising CDR1-L of sequence SEQ ID NO: 378, CDR2-L of sequence 'WAS', and CDR3-L of sequence SEQ ID NO: 379. V D1 is a variable domain of heavy or light chain of a first immunoglobulin; V D2 is a variable domain of heavy or light chain of a second immunoglobulin; V D3 is a variable domain of heavy or light chain of said second immunoglobulin; V D4 is a variable domain of heavy or light chain of said first immunoglobulin; C L is a light chain constant domain of an immunoglobulin; C H1 is a C H1 heavy chain constant domain of an immunoglobulin; L 1 , L 2 , L 3 , and L 4 are amino acid linkers; and wherein the first and the second polypeptide form a cross-over light chain-heavy chain pair, and wherein V D1 and V D2 are both either variable domains of light chains, or variable domains of heavy chains, and V D3 and V D4 are both variable domains of heavy chains if V D1 and V D2 are variable domains of light chains, or V D3 and V D4 are both variable domains of light chains if V D1 and V D2 are variable domains of heavy chains; wherein said first or second immunoglobulin is an anti-CD3 antibody which comprises a heavy chain variable domain comprising CDR1-H of sequence SEQ ID NO: 6, CDR2-H of sequence SEQ ID NO: 7, and CDR3-H of sequence SEQ ID NO: 8, and a light chain variable domain comprising CDR1-L of sequence SEQ ID NO: 142, CDR2-L of sequence 'KVS', and CDR3-L of sequence SEQ ID NO: 11; and wherein the other of said first or second immunoglobulin is an anti-CD123 antibody which comprises a heavy chain variable domain comprising CDR1-H of sequence SEQ ID NO: 381, CDR2-H of sequence SEQ ID NO: 384, and CDR3-H of sequence SEQ ID NO: 382, and a light chain variable domain comprising CDR1-L of sequence SEQ ID NO: 378, CDR2-L of sequence 'WAS', and CDR3-L of sequence SEQ ID NO: 379. <EOS>