New fritless glaze compositions have been developed for floor and porcelain tiles from a new boron raw material obtained by calcination. The complexity of this type of composition also translates into complex behaviour during firing in which, concurrently or in partially overlapping form, very different processes take place, such as crystalline phase dissolution, the crystallisation of new phases, and sintering phenomena. This paper analyses the physico-chemical transformations that develop during the firing of these new glaze compositions, focusing in particular on the sintering process and sintering kinetics. A multi-step kinetic model was developed in this study to encompass complex glaze compositions (containing up to nine components). The model appropriately describes the sintering degree of progress of five materials (a boron raw material and four glazes) with temperature, in constant-rate heating experiments, determined using hot stage microscopy (HSM). For the three glazes with the lowest starting amorphous phase content, sintering was assumed to take place in three individual, parallel and partially overlapping, steps. Sintering of the boron raw material was described by a single step, whereas for the fourth glaze, with a starting amorphous phase content intermediate between that of the raw material and the other glazes, two steps were needed. The evolution of crystalline phase content with temperature was used to identify the sintering mechanisms in each step. For each step, the kinetic model, pre-exponential factor, and activation energy were determined and related to the composition of the materials. As a novelty, the Avrami–Erofeev model, which is usually applied in describing the kinetics of chemical reactions and phase transitions, was used to describe each individual step.