Making sense of the derived Fukaya category for Lagrangians with weak regularity is part of the question, which seems highly nontrivial. As a basic meta-principle, any two Lagrangian branes in the same derived category class must lie in the same homology class in $H_{n}(X)$, so the homology class is fixed. This still leaves open some ambiguity on the choice of local system (cf. Remark 6.8), and the question of which singular Lagrangians to include (cf. section 5.3, 5.4).