The present inventors have successfully prepared a library consisting essentially of a plurality of antigen-binding molecules differing in sequence from each other, the antigen-binding molecules each comprising an antibody variable region that has binding activity against a first antigen and a second antigen different from the first antigen, but does not bind to the first antigen and the second antigen at the same time. Use of the library of the present invention allows the obtainment of a variable region having enhanced ability to bind to the first antigen and the production of a bispecific antibody against the first antigen and a cancer antigen. Moreover, the present inventors have also successfully prepared an antigen-binding molecule comprising an antibody variable region that has binding activity against three different antigens, but does not bind to these antigens at the same time.