Phrasal prepositional verbs (three word phrasal verbs)

Hi people!

What would you call the following verbs? Phrasal prepositional verbs, phrasal verbs, three word phrasal verbs, or just phrasals plus a preposition?

Put up with = TOLERATE.

Stand up for = DEFEND..

Catch up with = DISCOVER SOME WRONGDOING AND PUNISH IT / CAUSE PROBLEMS TO SOMEONE..

Get up to = TO DO SOMETHING, OFTEN SOMETHING THAT OTHER PEOPLE WOULD DISAPPROVE OF.

In fact, my question is: do you consider each of these verbs to be a unit or would you say they are a phrasal verb + a preposition? How would you parse these phrasals? What would you call each of the elements by which they are composed? Here's my view: VERB + ADVERBIAL PARTICLE + PREPOSITION.

In my opinion, they constitute a unit, and since they have a meaning of their own should be regarded as only one phrasal. Indeed, in The Cambridge Dictionary they appear as a unit. Besides, if we were to replace these phrasals with a word or a phrase, these would stand for all three words, namely VERB + ADVERBIAL PARTICLE + PREPOSITION, and not just for the first two. That is to say, when rephrasing, we do not need to replace the phrasal by a word or phrase and add the preposition the verb carries. The preposition "belongs" to the phrasal.

Examples:

1a. He's so moody - I don't know why she puts up with him.

1b. He's so moody - I don't know why she tolerates him.

2a. It's high time we all stood up for our rights around here.

2b. It's high time we all defended our rights around here.

3a. They had been selling stolen cars for years before the police caught up with them.

3b. They had been selling stolen cars for years before the police found out and punished them.

4a. I wonder what those two got up to yesterday.

4b. I wonder what those two did yesterday.

Now, I think they are different from other verbal constructions, such as: keep up (with) = STAY LEVEL OR EQUAL, since, in this case, we can do without the preposition "with", as this sentence shows:

5a. He started to walk faster and the children had to run to keep up.

Here, an example with the same phrasal, but including the preposition and, of course, we can't omit it in this case:

6a. Wages are failing to keep up with inflation.(All examples taken from The Cambridge Dictionary).

Now, if we were to replace this phrasal by another word or expression, the preposition would still be needed.

E.g.,

5b. He started to walk faster and the children had to run to stay level with him.

6b. Wages are failing to stay level with / stay equal to inflation.

What do you think?

Thanks a lot!

Mara.