For most of the East-Bay-to-South-Bay segment (from Santa Clara to around Fremont), there is only one track. That's not unusual in freight rail, but what's missing here are passing points: Long sidings where one train can get out of the way of a passing train.
Also, Union Pacific owns the tracks used by the Capitol Corridor, so priority becomes a question: Yes, passenger rail is supposed to be higher priority, but UP can (and does) charge Amtrak for using the rails. Railroads can (and have) demand that passenger railroads pay to build/upgrade infrastructure as a condition for running more passenger trains.
So yes, it would be doable, but it would be _expensive_.
If you've been to Oakland BART, you've probably seen that in an around that part of Oakland, there are two sets of freight tracks, one set very rarely used.
I ride CC every day and it is not that often delayed by freight. But I will switch to BART when it opens in Milpitas because that will be faster and cheaper and with much more frequent service.