1. Keep on: to continue. It is typically used to talk about a habit.
E. g. I have to keep on studying for another hour or so before I can go to the beach.
2. Go on: used for "continue" as well.
E. g. Will you go on watching the movie after I leave?
3. Keep on doing something: continue doing
E. g. Keep on stirring until the liquid comes to a boil.
4. Keep something up: continue at the same rate
E. g. If you keep those results up you will get into a great college.
5. Stick to something: continue doing something, limit yourself to one particular thing
E. g. You will lose weight if you stick to the diet.
6. Carry over: continue on a subsequent day, page, etc.
E. g. The party went all night and carried over to the next day.
7. Carry on about: continue in an annoying way
E. g. My father’s always carrying on about how I need to go back to school.
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