Short answer. No. Rule 11, Section 11 allows a defendant only one motion for extension of time to file an answer, granting at most thirty additional calendar days for meritorious reasons. A second motion for extension to answer is not authorized by this rule, regardless of how compelling your reason for needing more time is.
What the law says
A defendant may, for meritorious reasons, be granted an additional period of not more than thirty calendar days to file an answer. A defendant is only allowed to file one motion for extension of time to file an answer. A motion for extension to file any pleading, other than an answer, is prohibited and considered a mere scrap of paper. The court, however, may allow any other pleading to be filed after the time fixed by these Rules.
Rule 11, Section 11 — Extension of time to file an answer. Read the full provision →
The one-motion limit
Rule 11, Section 11 states the limit directly: a defendant is only allowed to file one motion for extension of time to file an answer. This is a hard cap on the number of extension motions specific to an answer, not a limit on how many days you can request within that single motion. Once that one motion has been filed and ruled on, the rule does not provide for a second bite at requesting more time to answer.
How much extra time the single motion can buy
The extension itself is also capped. The rule allows a defendant, for meritorious reasons, to be granted an additional period of not more than thirty calendar days to file an answer. So even the single permitted motion is not open-ended — it can add at most thirty calendar days, and only where the reasons given for needing that time are meritorious in the first place.
Why other pleadings are treated differently
The rule treats extensions for an answer very differently from extensions for other pleadings. It states that a motion for extension to file any pleading, other than an answer, is prohibited and considered a mere scrap of paper. So the one-motion allowance for an answer is actually more generous than what the rule permits for other pleadings, where an extension motion is not even recognized as a valid filing. The rule does add, though, that the court may still allow another pleading to be filed after the time the Rules fix for it.
What this means if you're past your one extension
If you have already used your one motion for extension to answer, Section 11 does not give you a second one to fall back on, no matter how genuine your continuing need for more time is. Needing additional days does not by itself create an exception to the one-motion limit the rule sets, so anyone in that position is dealing with a hard limit rather than a flexible one that adjusts to how much time is actually needed.