Is it possible to diversify my fund's bank account to a set of additional banks to reduce the risk of bank failure like with SVB?

Though it is possible to diversify your fund's bank accounts, it's not a realistic option for the small funds of emerging managers. First, your banking options are very limited. Most big banks don't want to work with emerging managers, have excessive fees and are very difficult to deal with. Second, it's a big pain for you to manage multiple accounts operationally. It's not only going to be more expensive due to the added fees, but it creates a lot of treasury and compliance lift for your firm and for your fund administrator. For example, the administrator would need to reconcile multiple bank accounts on a regular basis which more then doubles their work and their fees. Finally, the majority of emerging managers the operational experience to handle this level of complexity or the time. Once an emerging firm becomes an enduring firm, you can afford to hire treasury and accounting resources in house and you can experiment with more complexity like this.

Finally, the risk that you're trying to hedge against is minimal because:

1) VCs don't have a lot of money in the account for a long period of time. If they do, this is an indicator that they are mismanaging their capital call schedule which then creates a major drag on metrics like IRR.
2) By managing the capital call schedule well, it's unlikely that the bank account will have more money your bank account for an extended period of time beyond what's insured by FDIC
3) Changing bank accounts is fast and relatively easy. We had Decile Partners on SVB during the crisis and we migrated them off SVB in less then a week because bank accounts are pretty easy to change later.