Top-quality planning in general and quotient top-quality planning in particular deal with producing multiple high-quality plans while allowing for their efficient generation, skipping equivalent ones. Prior work has explored one equivalence relation, considering two plans to be equivalent if their operator multi-sets are equal. This allowed omitting plans that are reorderings of previously found ones. However, the resulting sets of plans were still large, in some domains even infinite. In this paper, we consider a different relation: two plans are related if one's operator multiset is a subset of the other's. We propose novel reformulations that forbid plans that are related to the given ones. While the new relation is not transitive and thus not an equivalence relation, we can define a new subset top-quality planning problem, with finite size solution sets. We formally prove that these solutions can be obtained by exploiting the proposed reformulations. Our empirical evaluation shows that solutions to the new problem can be found for more tasks than unordered top-quality planning solutions. Further, the results shows that the solution sizes significantly decrease, making the new approach more practical, particularly in domains with redundant operators.