Final answer:
Active transport enables the movement of glucose into a liver cell against its concentration gradient, utilizing glucose transport proteins, particularly GLUT4, which is regulated by insulin.
Step-by-step explanation:
The transport mechanism that could be used to transport more glucose into a liver cell that is already packed with glucose is active transport. This is because active transport allows molecules to move against their concentration gradient, meaning that glucose can still enter the liver cell even when the concentration inside the cell is higher than in the blood. In the liver, glucose may be stored as glycogen or further metabolized. Glucose transport proteins, or GLUTs, facilitate the transport of glucose through the plasma membrane. Specifically, GLUT4 is a glucose transporter that responds to insulin by moving to the plasma membrane to increase glucose uptake into the cell against its concentration gradient.