Witte de With, De Ruyter, and Jan Evertsen were determined to prevent another collapse, like what happened at the Battle of the Gabbard, in June 1653. They had felt like Tromp had lost control of the battle, and that the situation had turned into chaos. In the ensuing rout, the English captured or destroyed many ships. At Scheveningen, after Tromp's death, the Dutch understood that they were losing the battle. Instead of a rout, de With and his fellow admirals formed a rear-guard, and kept he losses and damage down, from what they could have been.
There is some indication that the Dutch had also fought in a line, although not in as disciplined manner as the English. The Dutch apparently had the advantage of the wind, at the beginning of the Battle of Scheveningen (also called Ter Heide), and attacked first. Like the English, the Dutch also broke the English line.
The results of either side breaking the line were less dramatic than what happened in the latter 18th and early 19th Centuries. To take advantage of breaking the enemy's line, you must concentrate on the ships on either side of the break, with several ships against one.
The Dutch usually practiced concentration and mutual support, but in this case, they kept their line intact, so that breaking the opponent's line did not have any dramatic effect. The main result of the four "passes" were that the smaller and more lightly armed Dutch ships accrued accumulated damage until they were not able to continue the battle.