Can we use mechanical pulleys to increase load tension?

Fig. 5. Spanish burton.So now try your skills on this pulley system, Fig. 5, called the
"Spanish burton". It is shown in Leonardo da Vinci's notebooks. What's
the number of rope segments 'supporting' the load? That's hard to count,
for only two forces from one rope act directly on the load. That "count
the ropes" rule is useless for anything other than block and tackle
systems. But the analysis of this system (or any pulley system) is easy.
First assume the system is in equilibrium (either at rest, or with
everything moving at constant speeds). Start at the right, calling the
tension in the right rope F. This rope passes over the pulley second
from the right, exerting an upward force 2F on that pulley. So, to
maintain equilibrium, the rope acting downward on that pulley must have
tension 2F. At the next pulley the downward force is 4F, and at the next
it is 8F, and by the time we get to the last pulley, the downward force
must be 32F = L. So the mechanical advantage is 32, and there are
nowhere near that many ropes or even rope segments in the system. (There
are 5 ropes and 10 segments.)