Full Definition of solar system : the sun together with the group of celestial bodies that are held by its attraction and revolve around it; also : a similar system centered on another star
Wouldn't object on the higher end of this range be regarded as a brown dwarf, making this system a binary star rather than a planet system?
Perhaps if it doesn't make it as a star, then it's not binary? It's not quite a planet system, but maybe one can call it a "Solar system"?
[1] https://en.wikipedia.org/wiki/Brown_dwarf
This might be interesting. In the same article, they call a pair of brown dwarves a "a binary system" rather than a binary star.