Is it possible to have a star orbiting around a brown dwarf? I know a single star is almost surely more massive than a single brown dwarf, but consider a case: a very small star is orbiting a very massive brown dwarf which has a very massive moon, such that the total mass of that brown dwarf and its moon is larger than that of the star. Not counting capturing, is this type of system possible (formed naturally)?
Yes

If a brown dwarf count as a star in this case, the solution is as easy as a smaller brown dwarf orbiting a larger one.

If not, it is still possible if you have two brown dwarfs orbiting close to each other, both just too small to be red dwarfs, together out-massing an orbiting red dwarf, just large enough to be counted as a star.

While I have no example of such a system, the Alpha Centauri system has to closely orbiting stars, with a more distant star orbiting, and Luhman 16 is a system with two brown dwarfs orbiting each other.