I insisted on opening the door. - I insisted that I open the door.
I insisted on him opening the door. - I insisted that he open the door.
This thread has had me thinking about whether the following variants are possible:
? I insisted to open the door. (I insisted that I open the door.)
? I insisted for him to open the door. (I insisted that he open the door.)
Do those work for you, Piscean? I find them borderline acceptable. The pattern doesn't seem recognized in grammar books, though examples can be found.
The infinitival complementation pattern clearly works better with "demand" than it does with "insist." These are unquestionably good:
I demanded to open the door. (I demanded that I open the door.)
I demanded for him to open the door. (I demanded that he open the door.)
And of course the "on"-pattern doesn't work at all with "demand." What a curious state of grammatical affairs.
*[strike]I demanded on opening the door.[/strike]
*[strike]I demanded on him opening the door.[/strike]