We describe probably the simplest 3-manifold which contains closed separating incompressible surfaces of arbitrarily large genus. Two applications of this observation are given. (1) For any closed, orientable 3-manifold $M$ and any integer $m\,{>}\,0$, a surgery on a link in $M$ of at most $2m\,{+}\,1$ components will provide a closed, orientable, irreducible 3-manifold containing $m$ disjoint, non-parallel, separating, incompressible surfaces of arbitrarily high genus. (2) There exists a 3-manifold $M$ containing separating incompressible surfaces $S_n$ of genus $g(S_n)$ arbitrarily large, such that the amalgamation of minimal Heegaard splittings of two resulting 3-manifolds cutting along $S_n$ can be stabilized $g(S_n)-3$ times to a minimal Heegaard splitting of $M$.