Cumming plays campaign manager Eli Gold on the CBS drama, which was recently picked up for a third season.
He told the Los Angeles Times: "I would like to continue to get more of a glimpse into [Eli's] personal life. The great thing about him is that he keeps surprising us, and by 'us' I mean the audience and me."
Cumming added that Eli is a "very complex" character with "a lot of baggage".
"He has a lot of foibles... so I hope I am allowed to keep delving deeper to find out more about him," he said.
The actor also joked that he wants Eli to show off his musical prowess, as hinted at in earlier episodes.
"I... hope we get to see him play the piano, as Chris Noth's character [Peter Florrick] mentioned he was a concert pianist in the first episode we saw him!" said Cumming.
The Good Wife star Julianna Margulies has previously admitted that she expects "friction" in the third season, while the show's executive producer Robert King has revealed that the theme of the new episodes is "taking risks".
The third season of The Good Wife will premiere on CBS this fall.