We generalize the embedding of induced-gravity inflation beyond the no-scale Supergravity presented in ref. [1] employing two gauge singlet chiral superfields, a superpotential uniquely determined by applying a continuous R and a discrete ℤn symmetries, and a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields. We show that, increasing slightly the prefactor (-3) encountered in the adopted Kähler potential, an efficient enhancement of the resulting tensor-to-scalar ratio can be achieved rendering the predictions of the model consistent with the recent BICEP2 results, even with subplanckian excursions of the original inflaton field. The remaining inflationary observables can become compatible with the data by mildly tuning the coefficient involved in the fourth order term of the Kähler potential which mixes the inflaton with the accompanying non-inflaton field. The inflaton mass is predicted to be close to 1014 GeV.