  We present TransitFit, an open-source Python~3 package designed to fit
exoplanetary transit light-curves for transmission spectroscopy studies
(Available at https://github.com/joshjchayes/TransitFit and
https://github.com/spearnet/TransitFit, with documentation at
https://transitfit.readthedocs.io/). TransitFit employs nested sampling to
offer efficient and robust multi-epoch, multi-wavelength fitting of transit
data obtained from one or more telescopes. TransitFit allows per-telescope
detrending to be performed simultaneously with parameter fitting, including the
use of user-supplied detrending alogorithms. Host limb darkening can be fitted
either independently ("uncoupled") for each filter or combined ("coupled")
using prior conditioning from the PHOENIX stellar atmosphere models. For this
TransitFit uses the Limb Darkening Toolkit (LDTk) together with filter
profiles, including user-supplied filter profiles. We demonstrate the
application of TransitFit in three different contexts. First, we model SPEARNET
broadband optical data of the low-density hot-Neptune WASP-127~b. The data were
obtained from a globally-distributed network of 0.5m--2.4m telescopes. We find
clear improvement in our broadband results using the coupled mode over
uncoupled mode, when compared against the higher spectral resolution GTC/OSIRIS
transmission spectrum obtained by Chen et al. (2018). Using TransitFit, we fit
26 transit observations by TESS to recover improved ephemerides of the
hot-Jupiter WASP-91~b and a transit depth determined to a precision of 170~ppm.
Finally, we use TransitFit to conduct an investigation into the contested
presence of TTV signatures in WASP-126~b using 126 transits observed by TESS,
concluding that there is no statistically significant evidence for such
signatures from observations spanning 31 TESS sectors.
