SAN JOSE — A legendary development firm has proposed big new office buildings in north San Jose, one of several Silicon Valley regions undergoing a leasing, buying and purchasing boom.

Peery Arrillaga, a realty firm whose principals are John Arrillaga and Richard Peery, has proposed construction of three new large office buildings, along with a parking garage, on East Brokaw Road near Bering Street.

The new buildings would be an expansion of what the company has built so far on the development property, which is bordered by Highway 101, North First Street, East Brokaw Road and Bering Drive, and also includes the site of the former and now bulldozed Bay 101 casino.

“The original site development permit allowed the demolition of the card room and construction of 10 seven-story office buildings totaling 2 million square feet,” said Ruth Cueto, a San Jose city planner.

Two of the new buildings would each be eight stories, and the third would be four stories, according to the planning documents. “This is an amendment to that permit,” Cueto said.

Peery Arrillaga has proposed development of 608,000 square feet of buildings, plus the parking structure, in the newest phase of the project, city planning documents show. As is their custom, neither Peery nor Arrillaga commented for this article.

“It’s a very good indicator that there is strength in the market in the city of San Jose, and especially north San Jose,” said Erik Schoennauer, principal executive with Schoennauer Co., a land use and planning consultancy.

At present, one building totaling 117,000 square feet has been completed on the site.

The newest phase of the development would include three office buildings. Two would total 241,000 square feet, and the third would total 126,000 square feet.

At full build out of 2 million square feet, the development could accommodate 10,000 workers. The existing office building, plus the three new proposed buildings, could potentially be enough space for 3,600 office workers.

“Peery Arrillaga has a site plan that references future development and a future submittal,” Cueto said.

A number of tech companies have been expanding their operations in Silicon Valley and the East Bay lately.

Among those that are adding space in huge chunks: Cupertino-based Apple, Mountain View-based Google, Menlo Park-based Facebook and Seattle-based Amazon.

Facebook recently leased 1 million square feet in Sunnyvale in a vast expansion of its operations; it also has leased 940,000 square feet in the Ardenwood district of Fremont.

Amazon has created a 1 million-square-foot campus through a several leases in Sunnyvale.

Google’s expansions include Mountain View, Sunnyvale and a transit-oriented development in downtown San Jose near the Diridon train station.

Apple has been leasing space in several locations in Sunnyvale and Santa Clara, and has collected enough properties for an 85-acre campus in north San Jose a short distance from the Peery Arrillaga development.