No matter how hot you are.. as long as the girl is not emotionally invested in you she will be open to meeting other guys.
A big part of game is getting her to emotionally invest. I have little idea as how to make a girl to invest in you (think about it, if we knew a solid approach, then all of us would be drowning in pussy). But get the girl to invest in you. Really open to tips as to how to do it. But that's a big part of the game