You'd find that the n-folded paper is both too tick and to narrow to achieve a n+1 fold. You could still put it in the hydraulic press and apply plenty of force

You'd find that the n-folded paper is both too tick and to narrow to achieve a n+1 fold. You could still put it in the hydraulic press and apply plenty of force with it, but the points where you apply the force will be too clumped together; the press would not fold the paper, just squeeze it really, really hard, and probably deform it or tear it apart at places.