The results are presented of anelastic and dielectric spectroscopy measurements on large grain ceramic PbZr1−xTixO3 (PZT) with compositions near the two morphotropic phase boundaries (MPBs) that the ferroelectric (FE) rhombohedral phase has with the Zr-rich antiferroelectric and Ti-rich FE tetragonal phases. These results are discussed together with similar data from previous series of samples, and reveal new features of the phase diagram of PZT, mainly connected with octahedral tilting and its coupling with the polar modes. Additional evidence is provided of what we interpret as the onset of the tilt instability, when is initially frustrated by lattice disorder, and the long range order is achieved at lower temperature. Its temperature TIT (x) prosecutes the long range tilt instability line TT (x) up to TC, when TT drops. It is proposed that the difficulty of seeing the expected 1 2 111 modulations in diffraction experiments is due to the large correlation volume associated with that type of tilt fluctuations combined with strong lattice disorder.It is shown that the lines of the tilt instabilities tend to be attracted and merge with those of polar instabilities. Not only TIT bends toward TC and then merges with it, but in our series of samples the temperature TMPB of the dielectric and anelastic maxima at the rhombohedral/tetragonal MPB does not cross TT, but deviates remaining parallel or possibly merging with TT. These features, together with a similar one in Na 1/2 Bi 1/2 1−x BaxTiO3, are discussed in terms of cooperative coupling between tilt and FE instabilities, which may trigger a common phase transition. An analogy is found with recent simulations of the tilt and FE transitions in multiferroic BiFeO3 [Kornev and Bellaiche, Phys. Rev. B 79, 100105 (2009)].An abrupt change is found in the shape of the anelastic anomaly at TT when x passes from 0.465 to 0.48, possibly indicative of a rhombohedral/monoclinic boundary.