This paper examines a market with asymmetric information where there are many signals available and where both the costs of signalling and product value may depend on many privately known characteristics. Under a weak condition on the relationship between the marginal cost of increasing the signals and the product value, a separating set exists whereby the value of every seller's product is inferred from the seller's optimal choice of signals. The separating set constructed is Pareto-dominant and corresponds to recently proposed equilibrium notions in signalling and screening models.