  We generalise the covariant Tolman-Oppenheimer-Volkoff equations proposed in
arXiv:1709.02818 [gr-qc] to the case of static and spherically symmetric
spacetimes with anisotropic sources. The extended equations allow a detailed
analysis of the role of the anisotropic terms in the interior solution of
relativistic stars and lead to the generalisation of some well known solutions
of this type. We show that, like in the isotropic case, one can define
generating theorems for the anisotropic Tolman-Oppenheimer-Volkoff equations.
We also find that it is possible to define a reconstruction algorithm able to
generate a double infinity of interior solutions. Among these, we derive a
class of solutions that can represent "quasi-isotropic" stars.
