Here are some synonyms:
* Full to the brim
* Overflowing
* Chock-full
* Packed
* Saturated
Example sentences:
* The vase was brimful of colorful wildflowers.
* Her heart was brimful of joy after seeing her family again.
* The parking lot was brimful of cars, making it impossible to find a space.
The word "brim" refers to the edge of a container, so "brimful" literally means "full to the edge".