The use of additive manufacturing in construction can significantly reduce the speed of construction of an object, labor costs, waste, reduce the risks of industrial injuries, etc. Despite a number of existing advantages of these technologies, their implementation in construction is associated with various problems, one of which is the need to ensure the required adhesion strength of printed layers. There are a number of studies devoted to solving this problem and creating effective materials for additive construction production, mainly based on cement binders; to a much lesser extent, these studies are available in the field of mixtures based on gypsum and mixed (gypsum-cement-pozzolanic) binders. The purpose of this work is to develop a scientifically based technological solution for improving additive technologies for low-rise housing construction using gypsum-cement-pozzolanic mixtures (GCPS) by regulating recipe-technological factors that provide increased adhesion strength of printed layers. Based on the results of the research, a technological solution has been developed to improve the technology of additive construction production of GCPM by regulating the kinetics of the increase in plastic strength of the mixture when it is modified with a multifunctional complex additive, which makes it possible to ensure the viability of the mixture required for 3D printing in the range of 0–50 minutes, significantly reduce the defectiveness of the extrudate during the 3D printing process, and increase the adhesion strength of the printed layers. It has been established that the adhesion strength of layers printed without a technological break from the GCP concrete mixture, modified with multifunctional complex additive, is 65% higher compared to the base composition, and when a technological break lasts 6 hours, it is 25% higher, which confirms its effectiveness in additive manufacturing.