We study the collective emission of a few emitters (up to three) in a cavity. In addition to the radiation coupling responsible for sub- and superradiance, we investigate emitters additionally coupled through a joint carrier reservoir. For such emitters, typically embedded in a solid state environment, the carrier reservoir provides a continuous pumping mechanism for the steady state emission. We show that the statistical properties of the emitted light depend strongly on the interaction between the emitters and the reservoir. Unexpectedly, the presence of the reservoir enhances the coherence of the emitted light already for a few emitters. This results from the fact that the carrier reservoir introduces new many-body correlations to the electronic transition and in this way suppresses multiphoton processes.