In (heterodox) economic theory, discussions of dynamic stability contrast negative with positive feedback effects. With more complex relationships, stable and unstable sub-models are set up, the intuition being that stability in an integrated model would be determined by the stronger forces. Accordingly, a combination of two stabilizing mechanisms will normally be expected to reinforce stability. The present paper gives a simple counter-example to this intuition, first in a purely formal reasoning and then illustrating it in a specific economic context. Regarding the latter, two approaches are considered that have recently been put forward in the literature to tame Harrodian instability: one by monetary policy acting through (indirect) interest-rate effects, and the other by an autonomously growing, non-capacity-creating component of aggregate demand, which gives rise to the so-called supermultiplier. While the two mechanisms separately stabilize the steady state if they are sufficiently strong, their interaction will necessarily render it unstable.