The older concept is differentiating between transitive and intransitive. A more practical concept is about the valency of a verb and its hierarchical transitiveness.
Intransitive: valency = 1. Only one object, which is the source but zero targets:
[1]He died.
Transitive: valency = 2. One source object + one target object.
[1]She dyed [2]her hair.
Di-Transitive: valency = 3. One source object[1] + one target object[2] + one nested target[3].
[1]She gave [3]me [2]her hair.
[1]He wrote [3]me [2]an email.
Nested transitiveness:
{[1]He wrote [2]an email} [3]{to me}.
Hyper-transitive adventure of a verb am and nested verb rain:
I am afraid it will rain cats and dogs three more days after tomorrow before New Year's through Christmas by lots of havoc with continuous fury, with incessant fear.
[1]I am
[2] afraid{
[4]it will rain {
....
}
[3]with incessant fear
The complete tree:
[1]I am
[2]afraid{
[4]it will rain {
[5]cats and dogs
[6]three more days
[7]{
[10]after tomorrow
[11]before New Year's
[12]through Christmas
}
[8] by lots of havoc
[9] with continuous fury
}
}
[3]with incessant fear
reflected with more precise numbering
[1]I am
[2]afraid{
[2.1]it will rain {
[2.1.1]cats and dogs
[2.1.2]three more days
[2.1.3]{
[2.1.3.1]after tomorrow
[2.1.3.2]before New Year's
[2.1.3.3]through Christmas
}
[2.1.4] by lots of havoc
[2.1.5] with continuous fury
}
}
[3]with incessant fear