In Excel you can place multiple buttons in the spreadsheet and programmatically let each button access solver with a different configuration and solve for a different problem.
Did you try the dispatcher slots? There are
.uno:GoalSeek
.unoGoalSeekDialog
.uno:SolverDialog
(I very rarely use the Solver / GoalSeek, and cannot tell something from own experience here.)
There are open bugs/requests concerning the solver. See:
tdf#113360