Counting date range overlaps for individual dates within another date range

Hey folks

So, I have a system that tracks availabilities of space on digital screens.

I have a list of availability (stored as date ranges) for each screen.

Each screen has up to 15 lots of available space on a given day.

I am trying to count whether the availability exceeds 15 for a given day but I am comparing 2 date ranges and not a specific day.

How can I count the overlaps on each day between the list of date ranges (availbility) against the other date range and then see if this number is greater than or equal to 15?

Thanks in advance!