This is one of the examples from cambridge dict.
Do you play any other sports besides basketball?
Oxford dict consider "besides", "except for" and "aside from" are synonyms.
To simplify the discussion, assume there are 2 options, basketball and baseball. Are "aside from" and "besides" exchangeable in the example sentence? If yes, then "aside from" and "except for" are not exchangeable. Here is the inference
set_A (mathematically) denote the group of sports the guy loves.
"besides" implies that both of basketball and baseball belong to
set_A while "except for" indicates that the guy only loves baseball in the scope of available options.
Is my understanding right?