The main trunk lines are in Long Island are about 3-4 miles apart. Northwest of around Cupertino or so, the mountains edge too close to the bay shoreline for you to make a second trunk line viable. Your best bet would be plonking a line around about 85, but the right-of-way doesn't exist to actually hook that line up to the existing line in any useful way.
And outside of that, basically everything you'd consider plonking another path already exists with some service: BART runs up the east shore of the bay, as it does west of San Bruno Mountain. You have two mountain crossings covered by BART and one by ACE. The main missing things are curving BART back into San Jose and reactivating the Dumbarton Bridge.
I've wondered about running BART from Fremont to East Palo Alto and Redwood City via Dumbarton. Not sure what the ridership would be though. I looked at the Dumbarton bridge traffic and it's the least of the three bridges and pales in comparison to the bay bridge.
Still if you built that the gap between Millbrae and Redwood city is 12 miles.