Ahh, I think I see your problem.
So, taking the itinerary above as an example, the journey would be EWR-ICN/NRT return, correct?
Because EWR-ICN/NRT is much closer by the pacific route than the atlantic route, the MPM is based on the pacific route and you don't get enough allowance to go through BKK. If you were trying to do EWR-FRA-BKK-ICN (11745 miles), that would be way over the MPM since the MPM for EWR-ICN is only 8254 miles.
What you need to do instead is to specify SIN/BKK as the turnaround, and MAD as the stopover. BKK/SIN is the same number of miles as ICN. Something like this (if flying F):
JFK - ICN (OZ F) or NRT (NH F) - SIN (SQ F) then turnaround SIN - FRA/MUC/ZRH (SQ/LH/LX F) - MAD (stopover) - ZRH/MUC/FRA - JFK (SQ/LH/LX F).
should work, because the MPM will be based on JFK-SIN instead, which gives you a lot more miles to play with. The outbound through ICN will be 9773 miles, and the inbound will be 11879 miles using ZRH for both transits.
Bear in mind that as far as I know, it is only one stopover in addition to turnaround.
Things will be more complicated if they enforce the no-backtracking rule as well, but see if the above itinerary is allowable.
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The following is the list of MPMs as available on Expertflyer.
JFK-ICN MPM: 8254 miles
JFK-NRT MPM: 8084 miles (although there seems to be two different routing options, where the other one offers MPM of 12511 - check with Aeroplan)
JFK-SIN MPM: 11434 miles
JFK-BKK MPM: 10388 miles
JFK-HKG MPM: 9666 miles
and I think Aeroplan allows 5% over the MPM allowance.
So, the maximum you can fly each way is
JFK-ICN +5% MPM: 8666 miles
JFK-NRT +5% MPM: 8488 miles
JFK-SIN +5% MPM: 12573 miles
JFK-BKK +5% MPM: 10907 miles
JFK-HKG +5% MPM: 10149 miles
Then you can use
The Great Circle Mapper to plug in the routings and see whether it would be within the limit.