the concept with four magnets has been discussed a bit in our group.
In this scheme the bpms work in an optimal regime and, I think, a 
resolution of better than 100 nm and a precision of this order should 
be achievable, providing no rotation of the middle bpms occures during 
the movement - We have no excitation of the incline component (what is 
the main systematic in case of three magnet scheme); also, using the 
movers we do not care much about the dynamic range and can optimize the 
electronics to get the highest sensitivity (our goal was to exclude the 
movers).
Right now I see one big disadvantage of the 4-magnets scheme:
In the 3-magnets scheme we have to measure very accurately the magnetic 
field of the central ("spectrometer") magnet only, because in common we 
measure its deflection angle. In the 4-magnets scheme we have to 
measure the magnetic field of at least two magnets. That means worse 
accuracy and perhaps more equipment.
I think we have also to take into account what happens with the beam 
itself. I mean, we measure the position of the center of gravity of the 
beam.
So, we should be sure, that it "does not" move inside the beam because 
of dispersion or whatever during the deflection and the transversal 
shape of the beam "is not" changed. Actually I hope this effect is 
small.
But these are details, in common, I think the 4-magnets scheme is 
better.

Best regards

Alex