Gravity theories involving, besides the usual Einsteinian metric field
, a macroscopically coupled, finite range antisymmetric tensor field B
(munu) are studied as foils to the strong gravitational field predicti
ons of general relativity, We consider the minimal class of such model
s among the multi-parameter gravity theories recently introduced by Da
mour, Deser and McCarthy. In the limiting case where the range mu-1 of
the B field is much larger than the characteristic size of the system
, this class comprises two arbitrary parameters: the coupling length l
ambda, which measures the coupling of B(munu) to the baryon rest mass
density, and a dimensionless parameter b characterizing the deviation
of the 'physical' metric from the Einstein value. We show that when la
mbda is a few kilometres and b is of order unity this class of models
predicts strong-field deviations of order unity in the overall charact
eristics of neutron stars: radius, binding energy, surface red shift a
nd maximum mass.