Reciprocity is Vietnamese is usually expressed by nhau ('each other'). Ngô N. B. (1999: 175) provides the following examples (also LVSP), in which nhau occupies a position c-commanded by the matrix subject họ ([raised] object and indirect object positions, respectively):
7a. Họ giúp nhau làm bài tập. [EV: 175]
prn help eachother do homework
'They help each other do homework'
b. Thỉnh thoảng họ viết thư cho nhau. [EV: 175]
occasionally prn write letter give eachother
'Occasionally, they write letters to each other.'
c. Hai cái áo giống nhau nhưng một cái rẻ và một cái mắc. [LVSP: 325]
two cls shirt resemble each.other but one cls cheap and one cls expensive
'These two shirts look alike, but one is cheap and the other expensive.'
Nguyễn Đ. H. (1997: 137) mentions one other rather interesting example involving nhau, in which the reciprocal occupies the object position, and the thematic object is projected as a prepositional phrase:
8. Anh ấy kiện nhau với ông chủ. [NDH: 137].
prn dem sue eachother with prn boss
'He sued his boss (literally, he sued each other with his boss).'
Though (8) may be interesting, and (7) not unhelpful, there's a good deal more to find out. First off, I'd like to know what happens in other embedded subject cases, such as (i)-(iii) below.
[If these constructed examples are ungrammatical for some irrelevant reason, please excuse (and correct the idiocy), but the point should be relatively clear: is nhau licensed in finite complement clauses, in VP-complements to causative làm and làm cho? I'm assuming that these examples are all fine if nhau is replaced by a pronoun with disjoint reference.
(i) Họ nghĩ (là) nhau dã viết lá thư
prn think comp each other ant write letter
'*They thought that each other had written the letter.' [= 'They each thought that the other had written the letter.'
prn make eachother cry
'They made each other cry.'
(iii) Họ làm cho nhau nhảy.
prn make give eachother dance
‘They made eachother dance.’
Any advice, thoughts, most welcome!