You will have twice as many poles as actual magnets, but the flux will be weakened, due to the wider air gap at the consequent poles.
Also, the pole spacing will not be optimum, unless the consequent poles are considered when spacing the magnets.

Sorry the drawing is so crude. Using a scavenged transformer core and three sets of magnets spaced 120 degrees apart around the outside of the rotor, at 2400 rpm this would produce 120 full cycles per second.

It would make more sense to put a single rectifier diode on each winding, output those current pulses to a large electrolytic capacitor. Then use a power mosfet (or IGBT) to pulse the capacitor into a heavy 1:1 transformer with 50% duty-cycle 60hz pulses to get your desired AC frequency out of the secondary winding. It's just a simple chopper-inverter circuit.

Hope this helps.

There is no limit to the number of magnets or stators you can "stack" on the axle. It is not limited to just three poles. You can make as many layers to the stack as you want and then just add more transformer cores that are in parallel with the axle shaft. Like my cruddy ascii drawing here.

E ||
E ||
E ||
E ||

Around the circumference of the rotor, use and EVEN number of stator sets and an ODD number of rotor magnets. Each set or "stack" of stator poles is wired in series with a single rectifier diode and it feeds an electrolytic capacitor.

Then just wire it up like so and shuttle your power around to wherever you like.