Perovskites in the ternary system PbTiO₃ (PT)–PbZrO₃ (PZ)–Pb(Fe₀.₅Nb₀.₅)O₃ (PFN) have attracted close interest because they can display simultaneous ferroelectric, magnetic and ferroelastic properties. Those with the most sensitive response to external fields are likely to have compositions near the morphotropic phase boundary (MPB) which lies close to the binary join Pb(Zr₀.₅₃Ti₀.₄₇)O₃ (PZT)–PFN. In the present study, the strength and dynamics of strain coupling behaviour which accompanies the development of ferroelectricity and (anti)ferromagnetism in ceramic PZT–PFN samples have been investigated by resonant ultrasound spectroscopy. Elastic softening ahead of the cubic–tetragonal transition does not fit with models based on dispersion of the soft mode or relaxor characteristics but is attributed, instead, to coupling between acoustic modes and a central peak mode from correlated relaxations and/or microstructure dynamics. Softening of the shear modulus through the transition by up to ~50 % fits with the expected pattern for linear/quadratic strain/order parameter coupling at an improper ferroelastic transition and close to tricritical evolution for the order parameter. Superattenuation of acoustic resonances in a temperature interval of ~100 K below the transition point is indicative of mobile ferroelastic twin walls. By way of contrast, the first-order tetragonal–monoclinic transition involves only a small change in the shear modulus and is not accompanied by significant changes in acoustic dissipation. The dominant feature of the elastic and anelastic properties at low temperatures is a concave-up variation of the shear modulus and relatively high loss down to the lowest temperature, which appears to be the signature of materials with substantial local strain heterogeneity and a spectrum of strain relaxation times. No evidence of magnetoelastic coupling has been found, in spite of the samples displaying ferromagnetism below ~550 K and possible spin glass ordering below ~50 K. For the important multiferroic perovskite ceramics with compositions close to the MPB of ternary PT-PZ-PFN, there must be some focus in future on the role of strain heterogeneity.