In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of conditioning events which are consistent with the given initial assessment. Quasi additivity assures coherence for the obtained conditional probabilities. In order to reach our goal we define a finite sequence of conditional probabilities by exploiting some theoretical results on g-coherence. In particular, we use solutions of a finite sequence of linear systems.