Not sure what a silo basement is--though I have seen homes that have a (decommissioned) missile silo in the basement.

It's simplest to jack up the existing home, then excavate and build a new basement under it. Alternatively, you can deepen the existing basement and underpin in sections. But this will require a lot of hand labour and take much longer. (Previous thread at GW on this topic.)

In many circumstances, it will be cheaper to add on abovegrade space.

Here is a link that might be useful: Moving a house