Could this stellar system exist within 10-20 light years from Earth, undetected?

After reevaluating my sense of perspective on sublight interstellar travel, I'm thinking of moving my planet closer to Earth to cut down on travel time and fuel costs. However, the planet my colonists are traveling to and the solar system it presides in have some very specific conditions.

Firstly, the star system itself is sextenary, composed of three binary pairs. Secondly, all three pairs orbit a central mass black hole with a mass of about 315 suns. Thirdly, this large black hole had to at some point in the past go hypernova, bombarding my planet with high energy particulates that caused various forms of exotic matter to appear in the crust of this young, embryotic planet.

Could a system like this exist anywhere within 10-20 lightyears of Earth? What are the odds that we wouldn't have detected it by now?

EDIT: Taking the suggestion to change to a single binary pair, what's the closest two stars orbiting each other could be to our solar system without having been discovered up until now?

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Could this stellar system exist within 10-20 light years from Earth, undetected?

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