Sure.
Br. X likes Sr. Y. He does some research, likes what he finds and gets her wali's contact and goes and proposes.
Br. X likes Sr. Y. He becomes good friends with the brother of Sr. Y. He lets him know that he likes his sister, and it goes to the parents and they get married.
Br. X likes Sr. Y. He proposes to her (lets her know of his intentions) directly (while observing proper Islamic etiquette) and asks for the contacts of her
wali, which she gives to him. He contacts the
wali and they're married later. If she doesn't, then that means she isn't interested in the proposal.
Sr. Y likes Br. X. She proposes to him directly (while observing proper Islamic etiquette). (I.e. "I am interested in marrying you, here are the contacts to my wali if you're interested.")
Sr. Y likes Br. X. She thinks he might like her too. She goes to her dad to let him know, they contact the brother and a few months later they're married.
Sr. Y likes Br. X. She knows the brother's sister and gets information about him through her. She likes it, and once she knows she has a chance of marrying the brother, she goes to her
wali. They get married later.