Twombly requires that a claim be pled with plausibility. For a breach of fiduciary duty claim by directors, this means that the pleading must: (i) establish that the defendant was a director of the debtor (and, absent other facts, not merely a director of the debtor's parent) during the time period covered by the complaint and (ii) specifically aver the facts describing the allegedly violative events, transactions or occurrences. A mere "naked assertion" that defendants have aided or abetted a breach of fiduciary duty, without factual support for such assertion, does nor satisfy the Twombly standard.

Under Twombly, in a constructive fraudulent transfer claim, the complaint cannot merely aver that "the debtor received less than reasonably equivalent value." There must be facts pled that support such an allegation.

For preference claims, Twombly requires that facts supporting each element be pled. This includes dates, amounts and types of transfers.

For beach of contract claims, Twombly requires the averment of facts that identify the contract and the specific provision that was breached.

A claim for unjust enrichment (under New York law) requires the plaintiff to establish that equity and good conscience militate against permitting defendant to retain what plaintiff is seeking to recover. Twombly requires that the plaintiff specifically aver facts that support how this element can be established.

New York does not recognize deepening insolvency as a cause of action. Deepening insolvency as a theory of damages cannot survive a motion to dismiss where the underlying claims are subject to dismissal due to insufficient plausibility under Twombly.