In a frictional environment, the frictional force between two surfaces depends on the normal force between them and the coefficient of friction. The coefficient of friction remains constant for a given pair of surfaces.
If the force applied to an object in a frictional environment increases, the frictional force can also increase, up to a certain point. The reason for this is that the frictional force opposes the relative motion between the surfaces in contact. When the applied force is small, the frictional force matches the applied force, preventing the object from moving. As the applied force increases, the frictional force also increases to match it, up to a maximum value known as the maximum static friction.
The maximum static friction is proportional to the normal force, which is the force exerted perpendicular to the surface. If the applied force continues to increase beyond the maximum static friction, the object will start to move, and the frictional force will transition from static friction to kinetic friction. Kinetic friction is typically lower than the maximum static friction and remains relatively constant as long as the relative motion between the surfaces continues.
In summary, in a frictional environment, increasing the force applied to an object can increase the frictional force up to the maximum static friction. Once the object starts moving, the frictional force transitions to kinetic friction, which generally remains constant at a lower value.