In a clause commenting on or continuing a preceding clause, the predicate may be abbreviated to an auxiliary or several auxiliaries, either echoing those of the preceding clause or newly introduced, sometimes with additional predicate items: “I thought we had been there before, and we had (been)” [i.e., had been there before]. “The first trip exhausted us, and the second probably will too” [i.e., will exhaust us]. “He was thinning out his collection [of books]: authors often do” (1986 Oct. 30 Times 18/2). These second, isolated auxiliaries serve as propredicates, implying the full predicate of the preceding clause.

In addition to such common-core instances, a more limited pattern with a present participle of an auxiliary has been reported as acceptable in some varieties of British (CGEL 12.22n, CamGEL 100, 1523): A: Why don't you sit quietly? B: I AMdoing. Kim is being investigated by the police, and I think Pat isbeingtoo. I've been Rex's mistress for some time now, and I shall go onbeing, married or not. They have all volunteered, but I think some of them regrethaving. None of these seem possible in American, and the last, with having, is said to be acceptable to very few British speakers.

Propredicatedo

In common-core English, intransitive do is used as a propredicate for verbs without any auxiliaries: She volunteered, and hedidtoo.