Yes, the body can make more glucose transporters if needed. The beauty of the individual cells in our body is that they can adapt to both immediate and long term changes that we directly influence.
In the case of whether the body can make more glucose transporters, the answer is simply yes. However, it is not the body itself making more glucose transporters, rather, it is the cells responding to their immediate environment.
To provide some background, 13 GLUT transporters have been identified in the human body. These 13 transporters have been broken down into four classes. The only class that we will discuss here is Class I which contains the most well-studied GLUT1, GLUT2, GLUT3, and GLUT4 transporters. GLUT is a glucose transport molecule.
To specifically answer your question, it has been shown that GLUT2 (present largely on the surface of hepatocytes or liver cells) can be unregulated by the presence of glucose. What this means is that when the liver becomes saturated with glucose, GLUT2 on hepatocytes will bring sugar into the cell. The plethora of sugar will trigger a cascade of events which lead to a release of a specific protein that alters the regulation of genes encoding GLUT2. To be a little bit more direct, an increase in sugar leads to an alteration in gene expression which leads to more GLUT2 being produced by the specific cell.
In conclusion, the body can make more glucose transporters but it requires a stimulus. Without the stimulus, glucose transporters will remain the same.