Hey there @Dylan31850!
Because Calendly sees each account as an individual user, it will not allow overlapping Calendly events in an effort to prevent double bookings. However, we do have a Group event type that will allow multiple invitees to book the same time slot on one event type.
You can also set up a team page that includes multiple users that are actually your alternative email addresses. Then, create a round robin event type between your accounts so invitees can continue scheduling for the same time slot as long as one account has availability. Keep in mind, you will have to pay for each additional user.
Additionally, you can use a One-Off Meeting type to give priority to an event (this is for one invitee and is a single use link). This allows you to offer times outside of your normal availability and over “busy” events on your connected “check for conflicts” calendar. However, there will not be any way to book Calendly events over other Calendly events. Here is a video I made for you showcasing how to use a one-off meeting to meet your goal:
I hope this helps!