Recently this exchange occurred on the American radio show/podcast “On the Media”:
KATHRYN VAN ARENDONK: …. when you go about separating art from artist, you can then run into all of these problems where you love work and you love an understanding of that artist that turns out to not actually be at all who they were in life.
BROOKE GLADSTONE: Did I just hear you say “Louis C.K.”?
VAN ARENDONK: I may have done.
And this from a recent New Yorker article: “Araten acknowledged that, relative to sales, the Hatfield factory employed fewer people than it had done in the past.”
The “may have done” and “had done” are examples of what ace Anglo-American linguist Lynne Murphy calls “pro-predicate ‘do'” (which I’ll abbreviate as PPD). As she explains in a blog post, in expressing the same thought, British people would say, “I ate all the chocolate, even though I shouldn’t have done,” where Americans would say, “I ate all the chocolate, even though I shouldn’t have.” In the examples at the top, the normal American constructions would be “I may have” and “… than it had in the past.” (Lynne doesn’t mention this, but I think an American alternative in the first case is to extend the sentence with another pronoun–that is, “I may have done it,” or “I may have done so.”)
In her post, Lynne has a full explanation of the relevant grammar, as well as a quote from a scholar who has found that the construction only became popular in Britain in the 1920s. (By the way, the “pro” in PPD stands for “pronoun”; as with pronouns, the “do” stands in for another word, in this case a verb.)
Since starting this blog six years ago, I’ve been on the lookout for American uses of PPD, with very little results, until now. Over the last year or so, I’ve noticed a handful examples, the “On the Media” and New Yorker ones being the most recent. Will Americans soon adopt PPV more broadly?
They may do.
notoneoffbritishisms.com 
I’m once again fascinated to find a usage that seems entirely normal to me as a native American brought up by England-born parents. My favorite columns tend to be those where I don’t immediately see the issue being presented. They teach me about my idiolect, knowledge that might not be transferable but is at least of interest to me.
I wonder where this is heading?
I wonder where this is heading to?
Or, Brian Butterworth, where this is headed, as Americans would say.
Or, Brian Butterworth, ‘whither this is headed’, as pedantic Brits say. ☺
Or, Ben Yagoda: ‘with very few’ results, until now’, alternatively ‘with very little success, until now.’
I know! I’ll get me coat…
I find this interesting. I recognise that the forms with ‘do’ are British rather than American, but how widespread are they in current British English. I know I never use them. None of my friends, relations or colleagues seem to use them. To my ear this usage sounds prissy or perhaps just dated.