The mass transfer process of binary esters of acetic acid in polyethylene terephthalate (PET), polyethylene terephthalate with a high degree of glycol modification (PETG), and glycol-modified polycyclohexanedimethylene terephthalate (PCTG) was studied. It was found that the desorption rate of the complex ether at the equilibrium point is significantly lower than the sorption rate. The difference between these rates depends on the type of polyester and temperature and allows the accumulation of ester in the volume of the polyester. For example, the stable content of acetic ester in PETG at 20 °C is 5 wt.%. The remaining ester, which has the properties of a physical blowing agent, was used in the filament extrusion additive manufacturing (AM) process. By varying the technological parameters of the AM process, foams of PETG with densities ranging from 150 to 1000 g/cm3 were produced. Unlike conventional polyester foams, the resulting foams are not brittle.