No, staring at the same spot in the sky for a prolonged period of time will not result in the ability to see more stars. The number of stars visible to the human eye or any other living creature is primarily determined by the inherent sensitivity and resolving power of the eye, as well as the brightness and distance of the stars themselves.
When you stare at a fixed point in the sky, the eye's light receptors, called cones and rods, become saturated with the available light. This saturation effect means that the eye's ability to detect faint sources of light, such as distant stars, is reduced over time. In fact, if you stare at a dim star directly, it may appear to fade or disappear altogether due to the phenomenon known as the Purkinje shift.
Additionally, the night sky has a natural background brightness caused by factors like light pollution and airglow, which can limit the visibility of faint stars. These factors are not affected by prolonged staring.
While the human eye is a remarkable organ, it has limitations in its ability to perceive faint and distant objects. Advanced telescopes and imaging technology are used in astronomy to observe and capture the light from distant stars and galaxies that are beyond the reach of our unaided eyes.