Yes, you can use AP points for that itinerary. For 120K in First and 100K in Business you can do TPE-EWR/JFK-TPE plus two stopovers. Since it would be a reward booking, not sure why you care about "maximizing the miles"? You don't earn miles on reward travel.
Where are you trying to visit? NYC and FRA and NRT? Do you care where you connect, or are you trying to sample lots of *A airlines?