  We show how any finite-dimensional algebra can be realized as an idempotent
subquotient of some symmetric quasi-hereditary algebra. In the special case of
rigid symmetric algebras we show that they can be realized as centralizer
subalgebras of symmetric quasi-hereditary algebras. We also show that the
infinite-dimensional symmetric quasi-hereditary algebras we construct admit
quasi-hereditary structure with respect to two opposite orders, that they have
strong exact Borel and $\Delta$-subalgebras and the corresponding triangular
decompositions.
