Let's say there was a snow day earlier in the year, and school was closed. That day was supposed to be a cycle-day 2, and now you need to replace a professional day later in the year with a day 2. Let's go into the CALENDAR section while managing the school and see what we have.
You could be tempted to modify your "Professional Day - No Classes" special day, but don't! Remember that each special day can be applied to multiple days. You can see where a special day is applied by hovering its symbol.
In this example, we want to replace that May 5th Professional Day. Here's how those weeks look like:
The 4th must remain cycle-day 4 and the 8th must remain cycle-day 5. Let's first remove "Professional Day - No Classes" from the 5th and see what happens. We can do that by clicking that day, or dragging the special "Drag on calendar to clear" item atop the list of special days. We don't have to worry about messing users' calendar, changes we make under the CALENDAR section are not pushed until you save them.
As you can see, days after the 4th are now incorrect:
We'll create a new special day, using the "+" symbol on the right side. That special day will explain, with its title, that we're recovering an earlier snow day. We want that day to explicitly be a cycle-day 2, while at the same time pushing the expected cycle-day 5 to the next school day.
Assigning that new special day over May 5th, either by dragging its symbol onto that day, or clicking the day, shows us what the outcome is. The 5th is now a cycle-day 2, the 8th is back to cycle-day 5. Everything is good and we can save changes!