Using Excel to check for overlapping times

I am looking for a formula that will check for overlapping times for both staff as well as clients. I have found numerous solutions, but unable to find a solution that allows for someone to end 1 service at 11 AM and start a new service at 11 AM with the same client (or different clients). My formula shows a conflict in that case.
I am looking for 3 basic things:
Staff- I need to see if staff are billing for overlapping times with same or different clients (e.g. bill 8-11am for one service with a client as well as billing 10am-12pm for anything/anyone else)
Clients- I need to see if different staff are billing for overlapping times with a client
Duplicate billing- I need to be able to see if there are duplicate entries (double-billing)

Book2.xlsx

Thanks everyone!

Any ideas anyone?