Once a lease is extended

[Joshua Ingram]

What are the rules, formalities and curtousies behind this situation? A possible tenant is chosen and the lease is extended (refered to as Person A. You tell them once they sign and submit the security deposit that the property will be taken off the market. They are excited and claim they will sign it within a day. Meanwhile, you continue to show the house and Person B and Person C show extreme interest. They ask to apply and are eager to sign a lease should it be exteneded. Do continue to extended applications and leases or wait to hear the response from Person A? Before extending another lease?