In [54]: from astropy.modeling.models import Gaussian1D
    ...: from collections import OrderedDict
    ...:
    ...: class Gaussian(Gaussian1D):
    ...:     def _parameter_units_for_data_units(self, inputs_unit, outputs_unit):
    ...:         return OrderedDict([('mean', inputs_unit['x']),
    ...:                             ('stddev', inputs_unit['x']),
    ...:                             ('amplitude', outputs_unit['y'])])
    ...:

In [55]: g = Gaussian()

In [56]: g._supports_unit_fitting
Out[56]: True

In [57]: g2 = Gaussian() + Gaussian()

In [58]: g2._supports_unit_fitting
Out[58]: False