I can only assume that you are still on about the 16 pole single rotor arrangement as you give no other information.
If this is the case you have 4 coils in series per phase at present. To make it 6 phase you connect with 2 coils in series. That means winding each coil with twice the number of turns of 1/2 cross sectional area wire.
Take half the winding as before, with a star point made of 3 starts. Connect 2 coils in series per phase. That completes half the winding. Now for the remainder, connect 3 finishes together to form a star point then connect 2 coils in series per phase to complete the second half. You now have two 3 phase windings which you could connect to separate rectifiers to produce 3 phase parallel with the same characteristics of the original 3 phase series winding.
To make it 6 phase, just join the star points. By reversing half the coils they are 180 deg out of phase with the others.
I can't give you more information if it is a single rotor, they are not really designable as the flux density depends on too many factors. You can base it on your previous results.
The only difference you find will be a bit lower cut in speed as 6 phase. If cut in speed is already low you might reduce the number of turns a bit.
If the picture in that link is what you have, you have wasted a lot of winding space and could have used thicker wire, the coils are nowhere near touching.
Flux