This artist's rendition shows the new "Triangle Building," which would be built on the stadium's west side.
The newest pitch promises more revenue for the state down the line in return for tax-backed bonds now.
"The Cubs contribute $618 million annually to the economy of Chicago. Our studies indicate that our renovation of the park and the triangle development will mean an additional $66 million a year in economic activity," said Cubs Chairman Tom Ricketts.
Half the money -- $200 million -- would come from the growth in amusement tax revenue already charged to Cubs tickets.
"We did it for the Sox. We did it for the Bears. Why not do it for the Cubs," said Cook County Commissioner Ricardo Muñoz (22nd).
The "Wrigley Investment Now" plan calls for more than 1,000 union construction jobs, something labor leaders said their members need.
"This isn't about the Cubs and it's not about the Sox. It's not about North Side or South Side. It's about jobs," said Jorge Ramierez with the Chicago Federation of Labor.
On Monday, both the governor and the mayor were cool to the plan, but latter on Tuesday seemed to be warming up.
"The concept, everything is good, but we have to work out the financial things. Really, if that works out, then you better believe I'm all for it," said Mayor Richard Daley.
Part of the plan is to take advantage of space that's currently a parking lot on the west side of the field. There, the Cubs want to erect what they're calling the "Triangle Building," a venue for a Cubs museum, a restaurant and amenities for fans.
The development would also house other businesses, perhaps including a new Harry Caray's restaurant. The restaurant group on Tuesday compared its relationship with its current building owner to a "bad marriage" and said it was closing by next week.
"The Cubs are bringing -- they're the economic engine for the North Side, the city and the state, and we have to do everything we can to help them grow and help the state grow," said Grant DePorter, the restaurant's CEO.
The Ricketts family said it want to move quickly, doing any work on the stadium in the off season, with a goal of finishing the renovations and the new building over the next four to five years.