What Insurance Will Cover if/when "Corporate Veil" is Pierced?

[Vidit S.]

Hi All,

Context - I live in NY and invest in PA. Have a multifamily(2 units) in a LLC that was bought by the LLC directly. We are three partners and follow all the steps to protect the veil and also keep anonymity (one partner is a lawyer). Even then if corporate veil was ever pierced, is there an insurance that can cover my personal assets? perhaps commercial umbrella?

Note: have underlying liability of $1M already with the LLC as insured.