I just have a couple of dynamical questions that I'm pondering over:-

If we wanted to maximise the delta-V increments from each successive
gravity assist flybys in turn via the 4 giant planets Jupiter, Saturn,
Uranus & Neptune (much like Voyager 2's grand tour), what is the
maximum (theoretical) final Sun-relative solar system escape velocity
that a hypothetical interstellar probe could achieve, and what are the
dynamical considerations in such a case?

I know Voyager 1 is presently escaping the solar system at 3.6
AUs/year and Voyager 2 at around 3.3 AUs/year, though maximising final
escape velocities for these crafts was never a goal in their primary
missions of planetary encounter, but supposing it was : what are the
theoretical maximums we could achieve by accumulating delta-V gains
following each gravity assisted boost via the 4 giant planets in the
case of the two Voyagers?

On a hypothetical scenario, if we have a *manned* spacecraft of mass 5
x 10^6 kg with an initial approach speed of say 10 km/s plunging into
the gravity field of Jupiter on an optimum gravity assisted
speed-gaining trajectory , what is the theoretical maximum delta-V
that could be gained post-fly by? With the new higher, gravity
assisted boost, if this optimum speed-gaining exercise was then
repeated at Saturn, Uranus and Neptune, in turn (assuming a favourable
positional line up of those planets in their respective orbits) would
the cumulative final speed be sufficient for interstellar flight?!

Cheers
Abdul Ahad