  We prove that, for any finite set of minimal $r$-graph patterns, there is a
finite family $\mathcal F$ of forbidden $r$-graphs such that the extremal
Tur\'an constructions for $\mathcal F$ are precisely the maximum $r$-graphs
obtainable from mixing the given patterns in any way via blowups and recursion.
This extends the result by the second author~\cite{PI14}, where the above
statement was established for a single pattern.
  We present two applications of this result. First, we construct a finite
family $\mathcal F$ of $3$-graphs such that there are exponentially many
maximum $\mathcal F$-free $3$-graphs of each large order $n$ and, moreover, the
corresponding Tur\'an problem is not finitely stable. Second, we show that
there exists a finite family $\mathcal{F}$ of $3$-graphs whose feasible region
function attains its maximum on a Cantor-type set of positive Hausdorff
dimension.
