  Building upon the results of [R. Augusiak et al., Phys. Rev. Lett. 115,
030404 (2015)] we develop a general approach to the generation of genuinely
entangled multipartite states of any number of parties from genuinely entangled
states of a fixed number of parties, in particular, the bipartite entangled
ones. In our approach, certain isometries whose output subspaces are either
symmetric or genuinely entangled in some multipartite Hilbert spaces are
applied to local subsystems of bipartite entangled or multipartite genuinely
entangled quantum states. To prove that entanglement of the resulting states is
indeed genuine we then introduce novel criteria allowing to decide it
efficiently. The construction is then exploited to provide examples of
multipartite states that are genuinely entangled but not genuinely nonlocal,
giving further illustration for the inequivalence between entanglement and
nonlocality in the multiparticle scenario. It is also shown how to construct
genuinely entangled states which are unsteerable across certain bipartite cuts.
