I assume this to be some commercial or light industrial service and that the calculations per Art 220 are in proper order. Then the lookup is in Art 310, Table 310-**, depending your application. My first guess is Table 310-16. Look down the 75 degree colume to 310Amps which is for a 350 kcMil copper cable, Type (as listed at the top of the column). Paralleling this cable brings you to 620 amps. Make temperature corrections, if required. You may use the 90 degree rating to accomplish this. Remember parallel cables must be cut to the exact same length.
YOu can use the same size neutral, or size it based on calculation in Art. 220-22.
The grounding electrode conductor is based on Table 250-66, equivalent area for parallel conductors, which would be a 2/0 copper conductor.
Hope this helps.