Japanese is an agglutinative, head-final language.
English is more analytical language.
This means that some meanings that are expressed in English using modal verbs and subordinate clauses can be expressed with agglutinative conjugation in Japanese.
Since it's head-final, the conjugational morphemes are appended after one another (while in head-initial language they would be prepended) - this could explain why the order in which the markers are applied looks reversed in Japanese and in English:
"Did (PAST) not (NEG) want (DESI) to be (PASS) made to (CAUS) eat (root)"
tabe (root) -sase (CAUS) -rare (PASS) -taku (DESI) nakatta (NEG-PAST)
This form can be seen as analytical, made of two separate words:
- 食べさせられたく - being an adverbial phrase
- なかった - meaning "it was not that ~" and taking the adverbial phrase before it as an argument.
Which brings us to analytical forms in Japanese:
The forms with 続く, 続ける, 得る, いる, ある, おく etc. can all be seen as analytical modal forms, which take nominal/adjectival form as an argument.
It depends on the specific verb what form it will be:
- nominal/adverbial form 1 (連用形): ~続く, ~続ける, ~得る
- nominal/adverbial form 2 (so-called て-form): ~いる, ~ある, ~おく
These are distinct from the agglutinative conjugation forms since they are based of full-fledged verbs, whose grammaticalised meanings stem from their regular lexical meanings:
- 続く - "<something> continues", 続ける - "to continue <something>"
- 得る - "<something> is obtainable"
- ある - "to be" - as in "車が門の前に止めてある" - "the car has been parked at the front of the gate" (focus on the past action) (this form is less commonly used)
- いる - "to be" - as in "車が門の前に止まっている" - "the car is parked at the front of the gate" (focus on the current state - a result of a past action)
- おく - "to put" -> "to do <something> in advance"
They form sentences with subordinate clauses, and the main verb in each of those clauses may undergoes the agglutinative conjugation process.
Also, the meanings of the conjugational morphemes tends to be broader than the meaning of modal verbs. Causative can mean:
- "to make (order, force) <someone> do <something>"
- "to allow (agree for) <someone> do <something>"
- "to allow (make it possible to) for <someone> do <something>"
Last, but not least - in conjugation like this, we are limited with respect to combinations we can form - the following examples are wrong:
- X 食べられさせた ("made it that <something> has been eaten")
- X 食べさせさせた ("made <someone> make <someone else> to eat")
To express those meanings, we would need analytical forms, probably with some nominalisations and させる used as full-fledged verb (causative form of する), not as a morpheme.