One of the many difficult issues English students have to deal with is that of multi-word verbs. The accentual patterns of multi-word verbs are not as complex as their semantics, but some clarification is needed, nonetheless, especially when they come at the end of the IP, which affects the observance or not of the LLI rule.
The first distinction to be made is between prepositional verbs and phrasal verbs. In the first case, the preposition which comes after the verb does not generally change the meaning of it and it is not accented.
(113) 
What do you think about it?
On the contrary, in phrasal verbs the particle following the verb tends to change its meaning and is normally stressed.
(114) I won’t give up.
However, this division is not clear cut. There are phrasal verbs where the meaning of the verb is not changed (e.g. go in/out) and prepositional verbs in which the meaning is much more idiomatic, as in the following example.
(115) What do you make of it?
This is probably why Martin Hewings (2007) talks about one-stress phrasal verbs (ˈdream of, ˈhear from, ˈlive for, etc.) and two-stress phrasal verbs (ˌhang aˈround, ˌget aˈlong, ˌcall ˈback, etc.).
As regards the LLI rule, therefore, prepositional verbs pose no special problems since it is the lexical verb that gets the accent and not the preposition. This is not the case with phrasal verbs, which constitute an exception because the nucleus is located on a function word.
Let’s now turn to a few examples of how the use of phrasal verbs involves the breaking of the LLI rule.
(116) It’s a book about priestly difficulties and about the nature of a community, very like the one in which you grew up (James Naughtie; Aberdeenshire, Scotland).
(117) Because what if? What if we slip up? What if a kid gets out or he gets in? (Joshua Ferris; Illinois, US; reading from a story by George Saunders).
(118) A perfect little story that he just simply knocked off one day [1] (Richard Ford; Mississippi, US).
(119) When Andy started off, I think with good intention he wanted to be an actor or a writer (Ricky Gervais; Reading, UK).
As can be observed, in all the cases above the particle of the phrasal verb, despite being a function element, bears the nucleus of the IP.
Another type of multi-word verb is the phrasal-prepositional verb, which has the following structure: lexical verb + adverbial particle + preposition. In this case, the main accent is placed on the adverbial particle too, as in
(120) I’m certainly not willing to put up with her.
(121) I’ve never really got on with him.
(122) We failed because of the difficulties we came up against.
Here is a naturally occurring example of the phrasal prepositional verb.
(123) Mark and Lisa are the two teenagers he starts running around with (Andrew O’Hagan; Glasgow, Scotland).
The adverbial particle around clearly carries the nucleus. The preposition with remains stranded and unaccented.
(124)
–Do you think when you’re making a film about what you we’ll be able to get away with the censorship boards?
-Oh, I’d never think about it in terms of getting away with. It’s not a thought.
(Mark Lawson; London, UK. / David Cronenberg; Toronto, Canada).
[1] The final time adverbial is unaccented.