Increasing the Maximum Shank Dia
There are bits referred to as Silver and Deming bits.  They have a smaller shank than the actual bit diameter and are available at home centers or on line. They come in a traditional twist drill configuration, so they can be used for drilling metal. If you are working with wood then "paddle" or "spade" bits will work also. You have to use caution when drilling holes of a larger diameter than the drill was designed. The drill may not have the secondary handle needed to control the torque. The speed of a single speed drill may be too high to control the bit. You may also overload and over heat the motor to the point of failure.