You mean they ‘deserve’ not ‘ask’ for Rule 11 Sanctions. Right?
Yes, and demand them early.
My approach to litigation was always one of two things, depending on what the other side “deserved.”
If they had legitimate arguable case, my approach was always, “Let’s be adults... and work to find a common ground.... and I will be too unless, in the rare case, your client becomes childish, at which time I will work to destroy your case and your client.”
That attitude, and reputation, moved a lot of cases to reasonable settlements before there was even a filing.
If on the other hand, they opened with foolishness such as this, it was “make the opposition client regret the day their mother first smiled at their father” from day one.
One of my favorite was lis pendens petitions and pre-verdict, even pre-trial demands for certified financial accountings and their last 7 years 1099s from the plaintiff to demonstrate that the P had the financial capability to pay our extensive legal fees that a verdict might well impose on them.
Didn’t get those accountings approved too often, but it always did get the Ps attention, and a lot of dropped cases.