What the rule is primarily meant to prevent is those catchups where people quote a single post and respond to it. Then they quote another post and respond to it as another post when they could just as easily combined it with their previous post. Here is the precise wording I use for the rule:
My Standard Ruleset wrote:3. You may double-post, but further posting in a row is heavily discouraged. More specifically, this rule is intended to cut down on things that needlessly clutter the thread such as spamming one liner quotes when catching up. This needlessly clutters the thread and takes up vertical space. It also makes it harder to refer back to older posts due to paging. With the advent of phones, this is a popular and "easy" method to catch up, but there are ways, even on phones, to combine smaller posts into larger ones. Try using the draft feature in gmail (or another email client of yours) or the notes app (on iPhones) to compose your thoughts in one post rather than as a burst of several posts. If you have something really important to say, do not let this discourage you from posting, but please try to be a bit more restrained.
4. Players are expected not to excessively spam the thread. While no formal rules apply, there will be penalties for violating this rule. Remember, not everyone can be online all the time. Be sure to give your fellow players a chance to speak rather than drowning out the thread with posts. Furthermore, spamming the thread is inconsiderate to players who are behind. They will become further behind even though they may in reality be posting at a reasonable rate. Please remember to be considerate of your fellow players at all times.
So, it isn't exactly a hard requirement not to triple or quadruple post, but this is still enough to get people to be more conscious of these habits.