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Abstract It has become increasingly useful to answer questions in gravitational-wave astronomy usingtransdimensionalmodels, where the number of free parameters can be varied depending on the complexity required to fit the data. Given the growing interest in transdimensional inference, we introduce a new package for the Bayesian inference Library (Bilby), calledtBilby. ThetBilbypackage allows users to set up transdimensional inference calculations using the existingBilbyarchitecture with off-the-shelf nested samplers and/or Markov Chain Monte Carlo algorithms. Transdimensional models are particularly helpful when seeking to test theoretically uncertain predictions described by phenomenological models. For example, bursts of gravitational waves can be modeled using a superposition ofNwavelets, whereNis itself a free parameter. Short pulses are modeled with small values ofN, whereas longer, more complicated signals are represented with a large number of wavelets stitched together. Other transdimensional models have been used to describe instrumental noise and the population properties of gravitational-wave sources. We provide a few demonstrations oftBilby, including fitting the gravitational-wave signal GW150914 with a superposition ofNsine-Gaussian wavelets. We outline our plans to further develop thetBilbycode suite for a broader range of transdimensional problems.