Our new house has a beautiful cast iron farm sink with small drains and no disposal. Can we drill out bigger holes for drains and disposal to retrofit and make it functional?

You can try but I have my doubts, Is this porcelain over cast iron? Back to you. Tom

Mighty big task. If it is Cast Iron, as Tom asks, almost impossible without chipping the porcelain. Sell it on Craigslist and buy one that has the proper size holes. Check Craigslist for the sink too.