Is there a maximum possible size for an airplane?
It is no accident that the biggest birds are flightless. The ability to fly goes down with increasing size, so there is also an upper limit for aircraft. The main reason is that as size increases, masses go up with the cube of the size increase while the load-carrying structures like wing spar cross sections only grow with the square of the size increase. This power law is the simplest of the scaling laws.

Since the loads on an aircraft's wing depend not only on its size, but also on many more parameters (angle of attack, speed, aspect ratio …), there is no clear boundary, and advances in materials help to shift the size limit up. If one would try to build the biggest airplane in the world, the wingspan could easily be double of what todays biggest airplanes measure, but the utility of this airplane would be very limited.

Using this airplane for passenger travel would add more restrictions like the number of emergency exits and the maximum distance to the nearest exit, but this could be overcome by using several smaller fuselages. A double-hull airplane would also spread out the payload weight, so the wing would experience a reduced root bending moment. Going from this (source):



to this (source):



would immediately raise the size limit substantially. However, it would require new, wider runways to take off from. And adding more fuselages to the same wing will run into flutter problems soon.

The next indication could be designs which have been studied and deemed feasible but were eventually not built for economical reasons. Here the biggest are ground effect vehicles: Flying slowly in dense air pushes the size limit up. The Boeing Pelican was planned with 152 m wingspan, and Beriev proposed one with 2500 t take-off mass and 125.5 m wing span.

I would guess that a wingspan of 200 m is still feasible, and when spreading the weight even 500 m should be realistic, but totally unpractical. Taking a lesson from history, this would be a multi-hulled flying boat which flies in ground effect, similar to the (mono-hulled) biggest aircraft record holders in the 1920s.