Following three things can be done to increase the magnetic flux of the coil without changing the field of the bar magnet:

1. Increasing the area of coil: Increasing the area of the coil will allow more magnetic field lines to pass through it, thereby increasing the magnetic flux. This can be done by using a coil with a larger diameter or by adding more turns of wire to the coil, which effectively increases its area.
2. Moving the coil closer to magnet: Decreasing the distance between the coil and the bar magnet will increase the magnetic flux. As the coil approaches the magnet, the strength of the magnetic field experienced by the coil increases, resulting in a higher magnetic flux through the coil.
3. Change in position of coil: Tilting or rotating the coil relative to the magnetic field lines of the bar magnet can also increase the magnetic flux. The magnetic flux is maximized when the plane of the coil is perpendicular to the magnetic field lines.