He came in with a suitcase, packed to the gills with samples and demonstration products.
Wiktionary
To-the-gills Sentence Examples
The venous blood is conducted from the tissues to a large sinus on either side above the pallial groove, and from this sinus passes to the gills by an afferent vessel in each gill on the internal or pedal margin of the axis.
In the latter they accumulate, being held together and fastened to the gills by a white viscid secretion.
The purplish hue to the gills matches this species.