Is it permissible to propose to a girl if the suitor knows that there is another person who wishes to propose to her?

It is permissible to propose to a girl as long as no one else has proposed to her. However, if she has been proposed to, it is not permissible unless the first suitor gives permission, or abandons the proposal, or his proposal is rejected. This is based on the Prophet's (peace and blessings be upon him) saying: "A man must not propose over the proposal of his brother, until the suitor before him leaves, or the suitor gives him permission."