The only US-based carriers with a strong Asian presence are UA and NW, now a part of DL.

On DL you must purchase a Y, B or M fare (equivalent to Y, B, H on CO; the top three fare buckets) to have any chance of upgrading the flight across the ocean. And there is still a decent chance that it will not clear, just like with CO. In the DL case you'd have paid more money (potentially a lot more) for the higher fare to be upgrade eligible and there is still no guarantee. The DL/NW flight would route via NRT to MNL.

On UA they are implementing a co-pay system similar to CO's though I am not fully versed in the details. There are also SWUs which you would earn several of. The catch on those is that they do have a minimum fare bucket to be eligible, but it is not nearly as onerous as with the DL miles upgrades. The SWUs are great as they are essentially free upgrades and you get six for making 100K miles (1K status) and then two more for every 50K you fly on UA metal. That is almost enough for you to do your trips, though not quite. Like with everything else in life there is a catch. In this case it is that UA does not serve MNL so your last hop will be in Y no matter what as UA doesn't have upgrades on its partners in Asia, and you might run out of SWUs leaving your other trips at the whim of mileage upgrades, with the associated co-pay.

Otherwise you can start looking at Asian carriers to get you there, but I have no idea how their upgrade programs work.