Hey there @Zach30121 -- great question!

This is how Calendly is designed. One of the core features on all plans (free and paid) is to avoid overlapping bookings. 

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 (this is not ideal for your rental use case, but I wanted to make sure to include it incase it helps you in another way, at some point!). 

You can also set up a team page that includes multiple users that are actually your alternative email addresses. Then you can either set up multiple event types under that team page (see: use a round robin event type as a one-on-one event type on a team page), and/or you can 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. 

You can read more about our plans, pricing and features on our Pricing Page! Note: an annual subscription will result in a 20% discount for all paid plans!

I hope this helps!