Each of these three-part verbs carries its own meaning, but they share one word-order rule. To come up with something is to invent or produce an idea or solution. To get away with something is to do something wrong and escape being caught or punished. To look forward to something is to feel pleased and excited about it before it happens. In all three, the parts stay together and the thing that follows lands after the last particle, never in the middle, so you come up with a plan, never "come a plan up with." (A few three-part verbs do take the object earlier, put it down to, take it out on, so check each verb as you learn it.) These phrasal verbs are neutral, everyday English; they sound more natural in speech and informal writing than their formal one-word cousins (devise, evade, anticipate).
Thinking things up
come up with /kʌm ʌp wɪð/ — The team came up with a clever solution just before the deadline.
get away with /ɡɛt əˈweɪ wɪð/ — She always gets away with arriving late because the manager likes her.
look forward to /lʊk ˈfɔrwərd tu/ — I'm really looking forward to the conference next month.
Not ""We need to come an idea up with quickly." (the object is jammed between the particles)" — say ""We need to come up with an idea quickly." (the object follows all three parts)". Three-part phrasal verbs are inseparable: the object always sits after the last particle. Say come up with an idea, not "come an idea up with."
Try it: Which sentence is correct? (We came up with a new strategy overnight. / We came a new strategy up with overnight. / We came up a new strategy with overnight.) Answer: We came up with a new strategy overnight. — 'Come up with' is inseparable, so the object 'a new strategy' has to follow all three parts. The other two versions drop the object between the particles, which never works with three-part verbs even though it feels tempting by analogy with separable two-part verbs like 'turn the light off'.
Tolerating and keeping pace
These three-part verbs describe coping and limits. To put up with something is to tolerate it without complaining. To keep up with something is to move fast enough not to fall behind it. To run out of something is to use it all up so that none is left. Whatever follows goes after the last particle — even a short pronoun like it — so you put up with it, never "put up it with." These three are neutral to informal; the single-word equivalents (tolerate, exhaust) feel more formal. That is true of these particular verbs rather than of phrasal verbs generally, since plenty of them (carry out, give rise to) belong to formal writing.
put up with /pʊt ʌp wɪð/ — I don't know how she puts up with the noise from the street every night.
keep up with /kip ʌp wɪð/ — It's hard to keep up with all the changes to the software.
run out of /rʌn aʊt əv/ — We ran out of time before we could finish the last question.
Not ""I can't put up it with any longer." (the pronoun is stuck between the particles)" — say ""I can't put up with it any longer." (the pronoun follows all three parts)". Unlike some two-part verbs, three-part verbs keep even a pronoun after the last particle. Say put up with it, not "put up it with."
Try it: Choose the correct sentence. (The service is terrible, but we put up with it because it's cheap. / The service is terrible, but we put up it with because it's cheap. / The service is terrible, but we put it up with because it's cheap.) Answer: The service is terrible, but we put up with it because it's cheap. — With 'put up with', even a pronoun object like 'it' comes after all the particles, giving 'put up with it'. The other options slip 'it' between the particles, which is exactly the mistake three-part verbs never allow, unlike some separable two-part verbs where a pronoun does go in the middle.
Try it: Which sentence uses the phrasal verb correctly? (She came up with a better title for the report. / She came a better title up with for the report. / She came up a better title with for the report.) Answer: She came up with a better title for the report. — 'Come up with' stays intact, so the object 'a better title' follows 'with'. The other two versions break the phrase apart by inserting the object between the particles, which three-part verbs never allow.