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This paper reports the successful extension of the basis of the X-ray multiple diffraction phenomenon in the assessment of structural phase transitions and the determination of thermal expansion coefficients along three crystallographic directions, using synchrotron radiation Renninger scans. Suitable simultaneous four-beam cases have accurately resolved the lattice-parameter variation in a nearly perfect single-crystal Rochelle salt using a high-stability temperature apparatus. Secondary reflections observed in the Renninger patterns, chosen by their sensitivity to the shifts in angular position as a function of temperature, have allowed the detection of a monoclinic to orthorhombic phase transition, as well as subtle expansions of all the basic lattice parameters, i.e. without having to carry out measurements on each crystal axis. The thermal expansion coefficients have been estimated from the linear fit of the temperature dependence of the lattice parameters, and are in agreement with those reported in the literature.