Abstract <p>New cases of seventh-order integrable dynamical systems homogeneous in terms of variables are presented, in which a system on a tangent bundle to a three-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which have a dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes the previously considered fields. Complete sets of both the first integrals and invariant differential forms are given.</p>