Extenuating circumstances is a hard sell most of the time. It can be done, but you would need to show catastrophic loss of income or an insurmountable amount of bills that forced the issue. Generally speaking we're talking someone got diagnosed with a serious illness and racked up hundreds of thousands of dollars in medical bills. The other situation would be the main breadwinner loses their job for multiple years in a row forcing a catastrophic set of circumstances.
You could theoretically get a conventional loan through FHLMC as they do not have waiting requirements you just have to get an "accept" through their automated underwriting system but the credit risk algorithm is pretty in line with FNMA's who has the 4 year waiting requirement. You could try, but it's unlikely to be approved until you hit that four year mark.
There are obviously non-qm alternatives that will allow you to get a mortgage with the BK but the rate reflects the risk. We're talking 5.5%+ at minimum to start for borrowers with excellent credit scores and low LTV loans.
