Water boils when it's vapor pressure equals atmospheric pressure (i.e., 760 mm of Hg) which is at 100 degrees Celsius. If the temperature is further increased, would the vapor pressure also increase or remain same?
Your question is phrased inconsistently. As you noted under "normal conditions", water boils at 100 degrees Celsius when the pressure is 760 mm of Hg. At that point there is no liquid water left and hence, technically, there is no liquid water to have a "vapor pressure."
Now steam (gaseous water) can have a pressure above atmospheric pressure if heated above 100 degrees Celsius in a closed container. (as Jon Custer has commented...)