You made me look, you, you … monster! 
and on the nautical side click pics to enlarge
How about expanding vertically rather than horizontally? Pile the airplanes one on top of the other and build biplanes, triplanes, etc…
Nope. The main purpose of a biplane configuration is to give more structural capability to the wings without increasing sectional thickness. However, this is done at the expense of greater drag and less lift; essentially, the upper wing is forcing pressure to be higher on top of the lower wing which detracts from the lift it develops.
The two main factors that limit the physical size of fixed wing aircraft are structural capability of the wing structure in lifting the aircraft and the amount of drag. (Others have noted logistical and practical considerations, such as the ability of fields to support aircraft of large wingspan, et cetera, but these could be addressed.) A traditional tube-and-wing layout has each wing supporting essentially half of the weight of the aircraft. This means that the loading out at the tip is minimal, but the further inboard you go the more force and bending moment the wing sees, and at the point (called the root) where it joins the fuselage (a structure called the wingbox) it sees very large forces and bending moments indeed. Although the size and strength of the wingbox itself can be increased, once you get out onto the wing itself you want to keep it as thin as reasonably possible to reduce form drag. (There is actually an optimum airfoil shape to keep pressure on top low without increasing drag, but all practical wing sections are a compromise.) Thus it is typically the size of the wing at or near the root that predicates how much loading a wing section can take, and that restricts how long the wingspan can be. By going to exotic lightweight materials like carbon fiber composite you can increase strength, but there is always the concern that at high stress levels the failure of any one element can result in structural failure compared to more ductile metal materials.
Chronos makes note of an interesting possibility in a wing that is essentially self-supporting, i.e. instead of being cantilevered out the load is distributed across the wing. His particular proposal–to tie together many aircraft at the wingtips–is, of course, absurd, but it does point to another solution to this problem, that being a flying wing, in which the wing is also the fuselage. First suggested (in a real engineering context) by Hugo Junkers, the flying wing has essentially no practical limit on size; as the structure is self-supporting in flight, stresses from aeroloading are minimal, and the wider and longer you make it, the less form drag is of concern. The main problem with the flying wing was stability; without the long tubular fuselage there is no place to mount a vertical stabilizer to give it yaw control, and thus, it is marginally stable or unstable in flight. This has been addressed in military stealth aircraft (which have primarily adopted a flying wing or blended wing body form for the superior RCS properties) by the use of active, fly-by-wire control systems; however, a failure or error in computer control would make these aircraft unflyable by human pilots, and the technology to develop this is expensive and specific to the aircraft design compared to the very mature and tried wing-and-fuselage which is aerodynamically stable.
Additional problems with a commercial flying wing or blended wing body design is the lack of window area, difficulty in egress in an emergency compared to a tubular fuselage, and the problem with placing passengers in the outboard sections where roll and yaw movement is more pronounced. On the other hand, FW and BWB aircraft can be designed to require significantly less lift to become airborne, requiring shorter runways and slower take-off and approach speeds. It is also possible (at least in theory) to mount the engines abaft and above the main fuselage, making the environment less noisy both for passengers and for people on the ground. Such planes also can have more interior space, permitting them to carry a larger fuel load or (depending on design) more passengers and cargo.
Stranger
LSLguy isn’t the maximum size of a commercial airliner defined by the standard 80m[sup]2[/sup] airport-standing box? IIRC the A380 is right on the limit.
CECIL!!!
sailor called me a monster. Wah. 
So you could construct a petawing?
This is a bit misleading. All aircraft must produce lift equal to their weight at all times they are in (vertically) unaccelerated flight.
A flying wing aircraft could well have greater wing area, which means it would tend to produce the necessary lift at lower speeds than typical aircraft. But this also tends to imply inefficiency at higher speeds.
True, but take it another way: the flying wing doesn’t have to lug around a big heavy tube that doesn’t provide any lift. Now, I’m sure there will have to be internal reinforcements around whatever cargo there is, but this reinforcement will almost certainly be less than the weight of a separate fuselage and reinforcement in the wings to carry that fuselage. Thus, for a given amount of stuff that you want to lift, you can use a lighter airplane, and therefore need less lift.
Sorry, I stand corrected; a flying wing or blended wing body need produce less pressure to develop adequate lift to achieve takeoff (compared to a tube-and-wing aircraft of the same weight).
Yes and no. Greater cross-sectional area does tend to imply more form drag; however, a properly designed flying wing should be able to almost completely eliminate or at least greatly attenuate the wave drag that makes transonic and supersonic flight so inefficient, without having to make compromises in fuselage configuration. This is, in fact, the reason why most supersonic aircraft are either of delta-wing configuration or use variable geometry wings swept back for high speed flight, as this increases lift from compression of the leading shockwave. The challenge would be finding some configuration of airfoil configuration and control surfaces that allow controllable low speed flight but efficient high speed flight, including possibly variable camber surfaces, oblique flying attitute, supercritical airfoil shape, et cetera.
Suffice it to say that this is an area of applied aerodynamics and aeronautical engineering that is far from mature, and assuming that the practical problems of can be addressed may offer considerable benefits over conventional commercial aircraft, albeit at extensive cost of research and development that few aircraft manufactures today are willing to invest in out of pocket.
Stranger
I was thinking more about flight at typical airliner speeds (say, 0.85 mach). Here, efficiency pretty well requires high wingloading; the large wing that produces good lift at low speeds is essentially always inefficient in cruise.
As a general rule in comparing like airfoil shapes, yes. However, there are a number of things that can be done to increase efficiency and promote clean, non-separating airflow over the wing surface.
Stranger
Agreed. An obvious one which has thus far vigorously resisted effective practical application would be the ability to alter the airfoil shape in flight. The best that can now be done is to deploy flaps, slats and so forth at low speeds.
There’s a, I guess you could it a “bioship”, in a movie or tv series that does just that.
If the goal is simply to get a large amount of stuff off the ground, large wings flying slowly is the way to go. If speed matters (as in the real world it almost always does) then you need thin wings and high wingloading, which pretty well guarantees higher takeoff and landing speeds.
But at high speeds the penalty for extra weight is small, so you get to carry lots of stuff (or lots of people) fast, which pretty much directly leads to the airliner shapes we are used to.
And birds do it rather well. Our attempts are rather pitiful by comparison, especially in view of how much more efficient than nature our best aircraft are.