The paper generalizes the construction by stochastic flows of consistent utilities processes introduced by M. Mrad and N. El Karoui (2010). The market is incomplete and securities are modeled as locally bounded positive semimartingales. Making minimal assumptions and convex constraints on test-portfolios, we construct by composing two stochastic flows of homeomorphisms, all the consistent stochastic utilities whose the optimal wealth process is a given admissible portfolio, strictly increasing in initial capital. Proofs are essentially based on change of variables techniques.