If row contains any value then add one to counter cell

I have two main response options in a survey question: A and B, and a handful of secondary options: D, E, F.

In my data export I'll have five columns. In a separate sheet I am using COUNTIFS to get totals, but am stumped as to the best way to deal with the secondary options. Essentially, if columns D, E and F contain ANY value I would like to add +1 to a counter cell. If columns D, E and F ALL contain values I still only want this to count as one (think of it like those three comprise the "other" category and don't need to be SUMMED as individual parts).