Existing approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions, as well as problem-specific desires that are apriori unknown, or at least difficult to articulate, for the end-user. We propose a general framework that can generate a set of of multiple (near-)optimal, diverse solutions for problems of a combinato-rial nature, that are further infused with user-selected quality notions. We call our approach solution engineering. A key novelty is that desirable solution properties need not be explicitly modeled in advance. We customize the framework to both the constraint programming and mathematical programming technologies, and subsequently demonstrate its practicality by implementing and then conducting computational experiments on existing test instances from the literature. Our computational results confirm the very real possibility of generating sets of solutions which otherwise might remain undiscovered.