When I send a rejection, some authors reply asking if I can recommend other agents for them to query.
I don’t reply to those emails. First, the book may not be good and my honest recommendation is revision. I can’t say that because an agent’s suggestion can feel like an executive order. I don’t have the right to dictate your career choices. Some authors would repost my reply and tell the world I’m a horrible person for trying to tell them what to do. Agencies run on reputation.
Second, I don’t always know who would be a good fit for the book.
Third, the author will take my suggestion too seriously. But my suggestion is no better than yours. I may know the agents, but you know the book. And I don’t know every agent out there.
Plus, some authors will query those agents saying “that agency referred me to you.” This isn’t a referral: where we believe in a book but it’s not a genre we rep. It would just be a personal suggestion between you and me.
Lastly, I don’t respond because I don’t have time. We love authors and want to support you as much as possible. But first priority goes to our authors we rep.