你所说的,实际上就是【及物动词的复合结构】,而这几个词 have,make,let,还有get也叫做【使役动词】.
它们典型用法搭配是：
have sb/sth do
doing
done
make sb /sth do
done
let sb/sth do
done
get sb/sth to do
doing
done
至于你所说的make sb/ sth done,这个结构确实有,但是,后面习惯搭配【反身代词作宾语】,再接【过去分词作宾补】.例如：
Jack,please 【make yourself known】 to all of us.
Mary put on a new dress to 【make herself noticed】 by others at the party.
祝你开心如意!