Welcome to the forum BBT723.
Yes, it is possible to design a generator based on your desired output power.
You can estimate each magnet output in watts according to the size and magnetic strength. For example, a neodymium magnet of N42 strength that is 2 x 1 x 1/2 inches in size has the potential to yield about 45 watts. Let's say that you have 24 of those magnets, (2 rotors with 12 magnets each) That could give you an alternator with about 1000 watts output.
Next, you would need 9 coils to build a 3-phase alternator with the 2 rotors of 12 magnets each. Then you choose the gauge of the magnet wire according to your desired voltage, whether it is 12, 24 or 48 volts output. Those 3 voltages are the most common because most people feed the rectified DC voltage output of the alternator into an inverter that converts it to 120 or 220 Volts AC.
The wire gauge that you choose for the coils depends on the total output power and on the voltage that you choose for your alternator. The higher the alternator output and the lower the voltage, the thicker the wire that you need to use.
For example, for the above alternator of a 1000 watt output, your wire size should be, 13, 14 and 15 gauge for 12, 24 and 48 volts respectively.
The number of turns per coil is determined by the desired RPM that you want your alternator to run. A higher number of turns will produce a higher voltage at a predetermined RPM.
Ed