I've been reading The Early Latin Verb by Wolfgang David Cirilo de Melo, where in a footnote he writes:
Synchronically, the participle here is best analysed as an elliptical perfect passive infinitive, although diachronically it is part of an older construction, the acc. with praedicātı̄uum.
Emphasis mine. The passage to which he refers is this:
(40) (Eunomia promises to help her son.)
Scı̄s tūte facta uelle mē quae tū uelı̄s. (Aul. 686.)
You know that I want the things done that you want.
Emphasis his, and not really relevant to this question. I would like to know more about this 'older construction, the acc. with praedicātı̄uum', as he puts it.
I've certainly come across the form that might be parsed as an ellipsis of the infinitive esse with adjectives (e.g., puto eum sontem (esse)), with past participles (puto eum amatum (esse)), with future participles (puto eum amaturum (esse)), and with gerundives (puto eum amandum (esse)); but de Melo claims that ellipsis is not the only possible mechanism.
So in addition to my broader question, which is just a request for more information generally, I am curious to know whether this accusativus cum praedicativo occurs in constructions that cannot easily be parsed as AcI + ellipsis: e.g., with the present participle (puto eum currentem).