The user asking this question has already solved the problem, they just want to know if there's a cleaner way. The answer is yes, but the real issue isn't the formula. It's that the data structure itself is working against them.
Three columns for three contact attempts is a common design, and it feels logical at first. Each attempt gets its own column, and you count across them with three COUNTIFS added together. It works. But it introduces friction every time you need to summarize, filter, or expand. Add a fourth attempt column, and the formula breaks. Add a new colleague, and the range updates are manual. The spreadsheet becomes brittle, and the person maintaining it becomes the bottleneck.
The cleaner approach is to normalize the data: store all attempt dates in a single column, with an adjacent column indicating the attempt number (1, 2, or 3). Then a single COUNTIFS can reference that one date column against the week range, and the attempt-number column can be left out of the count entirely if you only care about total attempts. If you do need to enforce the three-attempt limit, a simple data validation rule on the attempt-number column keeps it honest. This structure scales effortlessly, add more attempts by adding rows, not columns, and any summary formula stays simple and maintainable.
What this user is experiencing is the moment when a functional workaround becomes a recurring chore. The three-COUNTIFS solution isn't wrong; it's just not future-proof. And for anyone managing a team tracker, future-proofing isn't optional, it's what separates a tool that empowers from one that silently consumes time. Normalize the data once, and the formulas take care of themselves. That's the transformation worth exploring.