SAN JOSE — A legendary development firm has put the finishing touches on a development proposal that eventually will enable a mega tech campus to sprout in north San Jose where Google has already leased several big office buildings.

The first two phases of the vast tech campus near the corner of North First Street and Brokaw Road have been leased to Google through a deal between the tech titan and real estate company Peery Arrillaga, deemed to be one of Silicon Valley’s most successful developers.

Now, in its latest set of plans submitted to San Jose city planners, Peery Arrillaga has proposed the development of a third phase of the project where the developer aims to build five office buildings totaling a combined 1.3 million square feet of offices. These proposed offices would rise next to the four buildings that Google leased in 2019.

When combined with the 728,000 square feet of offices that Google leased, the entire project now is expected to total 2.03 million square feet, the plans on file with the city show.

“Nine office buildings and associated parking and amenities” would be the primary features of the entire campus when it is fully developed, according to Laura Meiners, a San Jose city planner.

The site plan for the project shows that several plazas, activity fields, and a ball field are among the amenities envisioned by Peery Arrillaga for the 30-acre development.

Google is said to be a choice candidate to lease some or all of the future offices that will rise adjacent to the buildings the search giant has already rented from Peery Arrillaga, according to several experts familiar with the Silicon Valley market.

The four buildings that Google leased within the campus are at various stages of construction.