COUNTIFs for a multi-column range?

[bumchicken]

On the Totals sheet, I'm using the COUNTIFs function to look at the Roster sheet and see where a name (matching that entered in row 8 for that column) appears over a range for a particular shift on weekdays and weekends respectively.
For example, C13 looks for C8 ("Laura" in this case) in the range D8-D21 and E8-21 on the roster (early shifts) AND where B8-B21 (day of the week) is "Sat" or "Sun."
The problem is if we want to insert more early shift columns on the roster - columns F and G labelled 'early extra.'

How do I make a formula that looks at the range from D8-G119 without having that formula become ridiculously long? It is very long already!

I read that using the SUM function with COUNTIFs is possible but I can't get my head around how to apply it to this example.

Any help would be massively appreciated.

[JohnTopley]

Example ....

Try

C13

=SUM(COUNTIFS(Roster!$D$8:$D$21,C8,Roster!$B$8:$B$21,{"Sat","Sun"}))+SUM(COUNTIFS(Roster!$E$8:$E$21,C8,Roster!$B$8:$B$21,{"Sat","Sun"}))