The previous versions of modsource did not have a proper implementation of the background emission in the cases where both the cosmic microwave background (CMB) and another source of continuum emission are present. The new version deals with such a situation in an improved way. In addition, the parameter defining the source continuum emission now corresponds to the level of continuum emission that can be measured in the spectrum of the source. In the previous versions, the continuum was assumed to be a blackbody and the parameter was defined as the temperature of this blackbody, i.e. it was not directly related to the level of continuum emission seen in the spectrum. The new behaviour is particularly convenient for interferometric observations, space observations, or in some cases single-dish wobbler observations that usually deliver spectra with reliable levels of continuum emission. Finally, the user now has the possibility to define a frequency-dependent source continuum emission by providing an array of continuum temperatures with the same size as the spectrum. By default, modsource still produces a baseline-removed synthetic spectrum. A new option has now been added to produce a synthetic spectrum that includes the source continuum emission.