follow through with something—complete smth. such as a plan, etc.; continue doing smth. until it is finished:
- Young children have a need to know that you will follow through with what you say.
follow up with something—
1. act further on smth.:
- Having a great idea and being able to follow up with it are two very different things.
2. do smth. after having done smth. else:
- The gymnasts perform compulsory routines today and follow up with individual events tomorrow.