Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are biorthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one ebit more than the average of the entanglement of the two states being superposed. However, for more general states, the situation is very different.