I'm not sure, but I think that можно means that something is "permissible" whereas возможно means that something is "possible". For instance: Мне можно это делать = "I am permitted to do this." (i.e. I am allowed to do this) мне возможно это делать = "I am able to do this." (i.e. I have the capability to do this. I'm smart enough, strong enough, etc...) Is this a correct distinction?