In practical terms, there's no limit. Current aircraft already have to be designed with consideration for parts bending under load. Taking that to extremes and allowing really massive deformations under load, you could make a thousand-tonne plane by sitting ten B744s side-by-side and sticking the wingtips together with something so flexible that they might as well not be connected at all. Technically it's one plane, but it flies just like ten B744s in a very tight formation. Clearly such a thing is possible, although finding a suitable runway may not be.
Obviously if you set out to design a plane with a thousand-tonne payload, there'd probably be more efficient ways than sticking a bunch of existing planes together - but the thought experiment shows that there is at least one way to achieve this goal. Beriev proposed the
Be-2500 ages ago, which would fit the bill and looks reasonably conventional. Boeing's Pelican is a similar concept. Both are designed to take advantage of the ground effect much of the time, while retaining the ability to fly at reasonable altitudes when necessary.