That depends on whether we can lose the positive charge. If we can't lose the positive charge on the rod, then no we can't. Because building a negative charge on the rod necessitates neutralizing the positive charge.
If we can lose the positive charge, then yes we can. The Glass rod is short on electrons relative to the protons in the glass molecules hence the positive charge. If we then give electrons to the rod, eventually there will be equal positive and negative charge or neutral charge. If we keep putting electrons on the glass rod, there will be more electrons on the rod then there are protons in the glass molecule, and the rod will have a negative charge.