With the "Conditions" of the screen sets, there's no way to do this. With formula-like conditions, you'd just say "round > 3", but you can't with the conditions panel of screen sets. You work around this limitation, though.
Create a screen set and set the screens in it to be what you want for rounds 1-3. On the conditions, select "Round" for Stage and set the round to 1.
Create another screen set, copying the first one, and set the Round to 2.
Repeat and set the round to 3.
Make a final screen set with screens that you want for round 4 and on. Don't add any conditions.
Ordering won't matter because the 1st set will be used for round 1 and only round 1. Likewise for screen sets 2 and 3. It should then default to the 4th set.