Second best choice with Solver

Solver is usually used to find the "best" solution. We aim to maximize value in a knapsack problem, or maybe minimize the scheduling time required for a set of jobs to be completed on some machines, and so on.

But what if we would like to know the second, or third best choice? Maybe we can gain some insights into our problem exploring suboptimal solutions. There are some caveats, but with a bit of VBA this is a feasible problem (pun intended).