Klaasen smashed 292 off 240 balls (39 fours and nine sixes) as the Northerns Titans were bowled out for 648 at Centurion.
The Free State Knights were 190-5 at stumps, with Gihahn Cloete unbeaten on 46. Lizaad Williams took 3-38 and Junior Dala – who made 56* with the bat – 2-10.
At Newlands, Verreynne scored 201* off 221 balls (21 fours and six sixes) as Western Province declared their first innings closed on 557-5.
The Boland Rocks were then bowled out for 202, with WP 12-1 in their second innings at stumps and leading by 343 runs.
In Port Elizabeth, the EP Warriors are 158-4 in their second innings after bowling out the KZN Dolphins for 285 (Jason Smith 45, Andile Phehlukwayo 68, Eathan Bosch 51).
The hosts, who have Matthew Breetzke (43*) and Diego Rosier (16*) at the crease, lead by 39 runs.
In Potchefstroom, Bjorn Fortuin took 4-38 for the Central Gauteng Lions to leave the North West Dragons in disarray on 143-9, still trailing by 219 runs.