On another forum I wrote the following on this topic. Maybe it is of help.
you have discovered that verb constructions with infinitive
have a lot of variants
1 modal verbs + inf (infinitive) - can do, must go, would know
2 verbs + to inf - have to do, plan to do
3 verb + acc (accusative) + inf - Let the children come to me.
4 verb + acc + to-inf - He wanted me to help him
5 verb + for + acc + to inf - He arrange for her to have a bath
Larger grammars give for each type of verb construction
a selective list of verbs, an explanation of the structure
and some examples.
Verb constructions are an important sector of grammar and when you
are interested in this point of grammar you have to make your own observations and complement the different lists.
I have short notations for the vcs (verb constructions):
a stands for accusative
t for to
i for infinitive
f for for
So you have the following vcs:
ai, ati, fati
The fati-construction is not so frequent. The most common verb
+ fati is to arrange for someone to do something/to have something.
In the sector verb + acc (accusative) + verb form
there are still other constructions, for example with past participle
to have something done
or with infinitive passive
Wikipedia often has this information:
The article does not exist. But you can ask for it to be created.
Another example with fati:
He motioned for her to enter.