General synonyms:
* Enlarge
* Amplify
* Exaggerate
* Enhance
* Magnify
* Boost
* Increase
* Promote
More specific synonyms:
* Exalt (to praise highly, elevate in rank or importance)
* Elevate (to raise to a higher position, rank, or status)
* Augment (to increase or make larger)
* Extend (to make larger or longer)
* Inflate (to make something seem larger or more important than it actually is)
* Embellish (to make something more attractive by adding decorative details)
* Enrich (to make something more valuable or interesting)
* Extol (to praise highly)
Negative connotations:
* Boast (to talk about oneself or one's achievements in a way that is arrogant or self-important)
* Puff up (to make someone or something seem more important than they actually are)
* Grandstand (to try to impress people by doing something showy or dramatic)
* Self-aggrandize (to try to make oneself appear more important or powerful)
The best synonym for "aggrandize" will depend on the specific context in which you are using the word.