On the north side there was also a plan to bridge San Francisco / Angel Island / Tiburon! Part of it still exists as Route 131.

https://www.flickr.com/photos/walkingsf/4047626058/

https://www.flickr.com/photos/walkingsf/4047626054/

https://www.cahighways.org/ROUTE131.html

Here you can see an idea of doubling-up the Bay Bridge, plus a view of the Southern Crossing / I-980 alignment: https://www.flickr.com/photos/walkingsf/4247129432/