Rear-ended, ambulance, total loss — at-fault party owns an LLC. Can I go after the business?

We were rear-ended with my newborn baby in the car. Ambulance came, my car was totaled, and we all have injuries. Baby seems okay so far, but we’re still monitoring. The at-fault driver admitted fault and the police report backs it up.

My attorney says the driver only has $25k per person liability coverage, and our policy matches it (we have $25k per person UIM). They’re telling me that’s basically all we can recover — but my injuries are serious and the whole thing has been traumatic. I was also newly postpartum and this hindered my recovery.

Complication: the at-fault driver was working at the time and runs a general contracting LLC. The business claims it’s licensed/insured, but my attorney says there’s no commercial auto policy, only personal.

Questions:

• Can I sue beyond policy limits if the driver has assets?
• Since he was working, can I pursue the LLC/business insurance anyway?
• What’s the best way to find out if there’s other coverage (umbrella policy, employer/business policy)?

Thank you.