Dual-gauge track could be used within the tunnels. It would also be possible to run both electrical systems, switching between whichever was needed.
Dual-gauge also crops up in Spain, where the high-speed rail network is 1435 mm standard gauge, but the traditional network is 1688 mm broad gauge. Electrical transitions are handled by the trains themselves (3 kV DC vs. 25 kV AC, both overhead line).
Yeah, within the tunnel the cost of having dual-gauge tracks and two electrification systems would probably be negligible compared to doubling the size of the tunnel. Getting the two signaling systems to work together and figuring out scheduling would be the bigger challenge there, I bet. BART is built on an assumption that it’s a completely separate system that never has to deal with level crossings or share tracks with other traffic.
A joint program of BART and the Capitol Corridor just announced the latest version of the long-in-development plans for a second bay crossing: https://link21program.org/
As currently envisioned, the project will provide either a new crossing for Regional Rail, a second transbay crossing for BART, or both.
My opinion: it should be a standard gauge tunnel for regional rail. In two years we’ll have electric trains running from San Francisco to san Jose; with some relatively simple upgrades to the infrastructure on that line and more funding, those trains could be running every 15 minutes or better, just as BART does. With some cooperation between transit authorities, it could run through a new tunnel under the bay and passengers could transfer to it just as if it were another BART line. High speed trains from LA could continue from SF to Oakland and onwards to Sacramento. And it’d cost much less than expanding the BART system.