Friction Ff=(F+mg)sinθ.
Supporting force FN=(F+mg)cosθ
When the pressure increases, it can be seen from the above formula that the supporting force is increasing, so A is correct;
We can think that the maximum static friction is equal to the sliding friction. If the friction coefficient is μ, there must be: (f+mg) sin θ < μ (f+mg) cos θ at the beginning.
When f increases, both sides increase at the same time, and the inequality relationship still holds, so the object will never move, so d is wrong;
Because the object is stationary and the friction force is equal to (F+mg)cosθ, the friction force increases with the increase of f; So, B is wrong; The object is always in equilibrium, so the external force is always zero, so C is wrong;
So the answer is: a.