Can one file a second Offer in Compromise after the first is rejected?

Yes, you can certainly file another Offer, especially when there is a change in your circumstances.   However, we should look at another possibility first.  When an Offer is rejected, you have 30 days from the date of the official rejection letter to file an appeal if you think the Offer Specialist was wrong in rejecting your Offer.  There is no cost to file an appeal, whereas if you file a new Offer, there will be a new $205.00 filing fee.  If, for instance, your income has significantly lessened, you have grounds for appeal since your income has changed from that which the Offer Specialist used.  If it has been more that 30 days since the Offer was rejected you can file a new Offer using your current financial information.  Either way, you have the ability to make sure the IRS knows your true situation and ability to pay.