When you have seen what could be a good idea for one of your authors, have you ever sent that idea, at the same time, to more than one writer?
I have, but never without letting the authors know. Occasionally I will have a publisher approach me with an idea for a book they would like to publish. This could be a new fiction series or a nonfiction title. Typically they are looking for a certain type of author, either an author with a specific platform or specific writing style. In those instances I will often send out an email to multiple authors at once to see who might be interested. I always, always let them know I'm talking to multiple people and will send over all who are interested and leave the final decision to the publisher.
There are other times, however, when I know that one of my clients would be perfect for the project and will approach only her. If she turns it down I will then talk to others.