depends ...
most likely if you work for one of the large companies (Boeing, Lockheed, ...) ... you're just too small, and they are too large for you to do much more than a "small" job; but then you are working on large scale projects (787, ...).
within large companies the best places to see more than a "small" technical job would be ground test, where you can design something, build it (well, oversee it being built), and use it; but then you're working on test rigs, rather than designing airplanes.
if you don't mind conceptual studies, try out advanced design; but then you're working with potenital airplanes, rather than aluminium ones.
smaller companies (Gulfstream, Bombardier) allow you to see more of the project, but it is very easy to get into a "small" technical job without much of a "big picture" view.
innovative companies (Rutan, Eclipse) might allow you a participate on a wider front.
but if you want to work if Al planes, and participate in all aspects of the engineering of the planes, i'd point you towards the very small mod shops around the country. these guys modify 'planes for special purposes and special customer needs (the after market of planes if you will). with these companies you can expect to see all aspects of your design; but, of course, you're aren't dealing with large original designs (smaller design projects with very different design constraints).
good luck