I recently (in 2013) received a From 4549-A from the IRS for tax year 2006? I had assumed that after 3 years, no review of or change to my taxes could occur, but clearly it is possible (for the IRS, at least) to make changes to returns much older than 3 years. Does receiving a 4549 for a particular tax year mean that I can make my own changes to the return (I significantly overpaid that year's taxes)?
No, you cannot request refund for more than 3 years back, since the statute of limitations is 3 years.
They can look back up to 3 years for any reason, up to 6 years if there's significant understatement of tax liability or under-reported income, and without limitations if there's suspicion of fraud.
You should not sign or agree to anything before you talk to a tax professional.