In what circumstances will a plaintiff be sanctioned for making a baseless claim?

In the ordinary case, a district court that would sanction a plaintiff for filing a baseless complaint might, in the exercise of its discretion, refrain from sanctioning the same plaintiff for filing a similar complaint containing, amongst viable claims, a baseless one. For that reason, were this an ordinary case, we would likely remand it to the district court for a determination as to whether it will persist in its decision to impose sanctions at all, and only if so for a determination of what those reconsidered sanctions should be. Cf. O'Brien v. Alexander, 101 F.3d 1479, 1492 (2d Cir. 1996) (finding that one of two representations for which counsel was sanctioned by the district court was sanctionable, but remanding the entire sanctions judgment "for the district court to reconsider whether and, in what amount, sanctions should nevertheless be imposed." (emphasis added)).