This article is interested in the scope for indeterminacies that originate from capital stock externalities in the technological set of the reference model of the multisectoral optimal growth literature. Sufficient conditions for local indeterminacies and oscillations are established and rest on a decreasing installation cost for capital units. The uniqueness of the steady state is also questioned and conditions for global indeterminacies are captured. Restrictions for balanced growth solutions are derived. Their uniqueness and their determinacy are established in the canonical model and the way externalities give rise to long-run indeterminacies and break uniqueness is detailed.