This paper proposes the Trajectory-Information Exchange Multi-Bernoulli (T-IEMB) filter to estimate sets of alive and all trajectories in track-before-detect applications with generalised superpositional measurements. This measurement model has superpositional hidden variables which are mapped to the conditional mean and covariance of the measurement, enabling it to describe a broad range of measurement models. This paper also presents a Gaussian implementation of the T-IEMB filter, which performs the update by approximating the conditional moments of the measurement model, and admits a computationally light filtering solution. Simulation results for a non-Gaussian radar-based tracking scenario demonstrate the performance of two Gaussian T-IEMB implementations, which provide improved tracking performance compared to a state-of-the-art particle filter based solution for track-before-detect, at a reduced computational cost.