  We construct free boundary minimal disc stackings, with any number of strata,
in the three-dimensional Euclidean unit ball, and prove uniform, linear lower
and upper bounds on the Morse index of all such surfaces. Among other things,
our work implies for any positive integer $k$ the existence of $k$-tuples of
distinct, pairwise non-congruent, embedded free boundary minimal surfaces all
having the same topological type. In addition, since we prove that the
equivariant Morse index of any such free boundary minimal stacking, with
respect to its maximal symmetry group, is bounded from below by (the integer
part of) half the number of layers and from above strictly by twice the same
number, it follows that any possible realization of such surfaces via an
equivariant min-max method would need to employ sweepouts with an arbitrarily
large number of parameters. This also shows that it is only for $N=2$ and $N=3$
layers that free boundary minimal disc stackings are achievable by means of
one-dimensional mountain pass schemes.
