interesting question. I don't know, if there's a universal answer, but will try to argument by plausibility:
One important criterion for a good solvent is that the absorbed component can be easily removed (i.e. using a low number of stages and reflux ratio).
Remembering, that we use extractive distillation only in difficult separations, it seems quite natural, that the 1st column will have a larger stage count than the 2nd.
It is true that first column must have larger stage than the second because of existence of azeotrope. Now for the subsequent column, the total number of trays mostly depend on the relative volatility of each component with respect to the light key component.
Usually the most difficult separation is done first while sequence of distillation columns are used. Usually more number of plates for the first column than subsequent columns.
While there are exceptions as well where first columns have less number of trays in comparison to subsequent distillation columns. E.g when A,B,C mixture is present and A forms azeotrope with B while B forms azeotrope with C then A and C may or may not form azeotrope. In such a situation first column require less number of tray columns