Adjustments to sumproduct to ignore if all entries at each date is blank

Hi there,

I am struggling with a formula to count the number of non-blank cells in a range of dates, however, excluding dates that have ONLY blank entries (04-01-2019 in the workbook).

Basically, I have a number of dates spread across the employees of 4 companies. For each company, I'd like to know how many employees were present over the period.

A "blank entry" corresponds to an absent employee, whereas an "employee name" represents a present employee.

Please see the enclosed sample workbook for a more detailed description.

Thanks,
Phil