For years I've used a travel vest - a vest with very numerous pockets. Most travel gear and outdoor clothing companies -- Travelsmith, Tilley, Magellan, Filson, and others -- make them. I especially like Tilley: expensive but well made and last forever.

These vests have so many pockets that you can stuff the equivalent of an extra carry on bag into them. You may end up looking like the Michelin man and waddle a bit , but you can get on the plane -- a vest is an article of clothing, and there's no rule against having a lot of stuff in your pockets. So far at least no security gate has ever said anything about my vest, though I have to put it on the belt since it usually has stuff in it that will set off the metal alarm. But once through security I just put it back on again.

If you don't like vests, some of these same companies make travel sports jackets or blazers which also have a lot of pockets you can stuff things in, though not as much as a vest.