I'm sorry, I don't know whether planesmen stack, but I want to clarify one thing:

You mentioned a guide that said planesman ability is limited to it's given tier.... I assume you mean the tier of the ship it's on. I want to make the point that (AFAIK) it's not the ability that's limited, rather it's the total reserve of air that's limited.

For a given SS, the maximum amount of air you can store is fixed, but the time it takes to replenish that air is determined by your planesman.

If your planesman is good, your air will fill faster. But once you're underwater it doesn't matter - the air you have, is the air you have. No matter the ability of your planesman your air will be consumed at a constant rate.

Basically, your planesman ability only matters when you are surfaced. And then, it only affects how fast you air refills, not how much air you can store, and not how long you can stay underwater. So the cap is the amount of air you can store, not the speed at which it refills.

I have no data to back this up, and I may be wrong, but that is how I understand the way a planesman works.