Yes. But it might not be satisfying...
In particular, you can have two co-planets orbit each other (by all rights the Earth Moon system should be considered co-planets; the Moon is larger than most moons in our solar system. But Saturn Titan is even a better candidate: Titan is 3200 miles in diameter and 80% more massive than the Moon).
Then they can orbit a much more massive object at some distance. Or alternatively, a much less massive object can orbit them.
As my comment above says; The Three Body Problem [3BP] is only a computational problem, it is difficult to solve 3 simultaneous differential equations.
That said, we already do know 3BP can be stable: I just gave two examples! The Earth-Moon-Sun was the first 3BP recognized and studied extensively by the guy that invented gravitational problems in the first place: Isaac Newton himself.
The Saturn-Titan-Sun system is another non-trivial example, and also stable. Titan is about half the diameter of Earth (the moon is a bit over one quarter the diameter of Earth). Titan is about 2.25% the mass of Earth (the moon is 1.2% the mass of Earth). Surface Gravity on Titan is about 85% of that on the Moon (this sounds counter-intuitive, but Titan is 44% less dense than the Moon).
The 3BP is only about us puny humans calculating whether such a system is stable or not: Obviously it is possible but in our examples (and what we know about other moons in our system), the stable ones have large factors of scale, at least as far as mass: factors of 20 or more.
In terms of mathematics, this allows orbits that cause small perturbations, so in laymen terms they basically cancel out or can be ignored, as long as we don't have any resonance patterns that cause an amplification of relative movement (so that some part reaches either escape velocity or gravitational collapse so they crash into each other).
but the mass factors should not concern you too much: Our Moon is 1.2% the mass of Earth but has a surface area that is 7.4% that of Earth; 14.7 million square miles; about 4 times the size of China (or USA). Plenty of space to support a population.
If the Moon were denser it would have a smaller radius and therefore a higher surface gravity. Platinum is a very dense element; about 3x that of iron and a noble metal (not very reactive). If nearly the entire mass of the Moon were Platinum (say except for a crust about a kilometer deep), the radius would be 934.9 km (instead of 1737.1), and the surface gravity would be 57% that of Earth. That might be enough to hold a breathable atmosphere.