In star systems with multiple stars, can you have different ‘solar systems’ for each star or each pair of stars?

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I’ve been watching some youtube videos on multiple star systems, and I’m very confused as to whether each of the stars can have their planets.

If two of the stars are in a binary configeration for example, I think they would have their own ‘planets’ together, however I don’t know if a third star separate to the first two would have it’s own stable system.

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