A　group　theoretical　model　is　proposed　for　linear/quadratic　coupling　between　order　parameters　which　arise　from　electronic　and　soft-mode　instabilities　in　doped　shape　memory　alloys,　together　with　coupling　to　symmetry　breaking　shear　strains.　This　model　is　tested　by　using　resonant　ultrasound　spectroscopy　(RUS)　to　follow　the　elastic　and　anelastic　anomalies　which　accompany　transitions　from　B2　to　B19,　9R,　and　incommensurate　structures　in　Ti50Pd50-xCrx　alloy　samples　(0≤x≤12).　The　pure　soft-mode　transition　gives　rise　to　an　incommensurate　structure　but　without　any　associated　changes　in　the　shear　modulus,　implying　that　coupling　with　shear　strains　is　weak.　By　way　of　contrast,　the　observed　pattern　of　softening　ahead　of　and　stiffening　below　the　martensitic　transition　is　typical　of　pseudoproper　ferroelastic　behavior　and　confirms　that　there　is　strong　bilinear　coupling　of　the　tetragonal　shear　strain　to　the　order　parameter　associated　with　irrep　Γ3+　of　the　parent　space　group.　The　second　order　parameter　has　the　symmetry　properties　of　M5-　in　TiPd　or　of　a　point　along　the　ς　line　of　the　Brillouin　zone　for　the　9R　and　incommensurate　structures　with　high　Cr　contents.　Comparison　of　shear　modulus　data　for　Cr-rich　samples　obtained　by　RUS　at　105-106Hz　with　previously　reported　Young＇s　modulus　data　obtained　for　different　samples　by　dynamical　mechanical　analysis　at　∼0.1-10　Hz　has　not　revealed　the　dispersion　with　frequency　that　would　be　expected　for　a　glass　transition　governed　by　Vogel-Fulcher　dynamics.　The　two　techniques　differ　in　the　magnitude　of　effective　applied　stress,　however,　and　differences　in　chemical　homogeneity　between　samples　or　decomposition　during　high-temperature　measurements　might　also　be　a　factor.　©　2020　American　Physical　Society.