Invent.
Make up
I was trying to make up a good excuse for being late.
Successfully communicate ideas.
Put across
It's an interesting idea and I thought he put it across well.
Save a certain amount of money/time.
Set aside
He puts some time aside each evening to read to his children.
Be surprised.
Take aback
I was a little taken aback at the directness of the question.
Happen, appear unexpectedly (with "Crop").
Crop up
A new problem cropped up.
Compensate. (2 prepositions)
Make up for
He bought me dinner to make up for being so late the day before.
Extinguish.
Put out
Be sure to put out your campfire before you go to sleep.
Start a journey.
Set off
What time do we set off tomorrow?
Deceive.
Take in
I can't believe she was taken in by him.
Fall asleep (with "Drop").
Drop off
I must have dropped off during the show, because I don’t remember how it ended.
Go towards something or somewhere.
Make for
They split up and the man made for the subway.
Tolerate (2 prepositions).
Put up with.
I simply can't put up with his behaviour.
To cause an alarm to ring.
Set off
I accidentally set the alarm off.
Resemble.
Take after
He takes after his father.
Delay (with "Hold").
Hold up
Something is holding up the work.
Be able to read/see/understand something.
Make out
I can't make out what he is saying.
Let someone stay in your house.
Put up
I can put you up for a couple of days.
Cost.
Set (somebody) back
The house set them back $200,000.
Give (someone) a job.
Take on
My company is taking new workers on.
Spend time doing nothing (with "Hang").
Hang around
I love hanging around with my friends.
Steal something and escape with it (2 prepositions).
Make off with
The thief made off with a valuable necklace.
Explain the cause of (2 prepositions).
Put down to
His failure was put down to a lack of interest.
Start and seem likely to continue.
Set in
This rain looks as if it has set in for the rest of the day.
Occupy space.
Take up
This armchair takes up too much space.
Be understood, assimilate, start liking (with "Sink").
Sink in
How many times do I have to tell you something before it sinks in?