Officially, there is no such thing as a "Chapter 20 bankruptcy" because the Bankruptcy Code only goes up to Chapter 15. Instead, "Chapter 20 bankruptcy" refers to debtors who file for Chapter 7 bankruptcy and then file for Chapter 13 bankruptcy after the Chapter 7 bankruptcy ends.
The name comes from the fact that the two chapters are combined: Chapter 7 + Chapter13 = Chapter 20.
There are two reasons people might want to file a Chapter 13 bankruptcy after a Chapter 7 bankruptcy. First, the advantages of both types of bankruptcies stack together nicely. People typically file for Chapter 7 bankruptcy to discharge their unsecured debts (like credit cards). People typically file for Chapter 13 to "lien strip" or reduce the amount of money they owe to secured creditors (like car loans).
The two advantages overlap very nicely. People often have both secured and unsecured debt. One goal of Chapter 20 is to discharge unsecured debts in Chapter 7 and then reduce the remaining secured debt in Chapter 13. Chapter 20 allows the debtor to make the most of the bankruptcy system.
The second reason to file for Chapter 20 is to extend the amount of time the debtor needs to repay secured loans. The debtor receives an automatic stay during a bankruptcy, a court order which prohibits creditors from trying to collect on their debt. In Chapter 7, the stay only lasts a few months because the bankruptcy ends in a few months. In a Chapter 13 though, the stay could last three to five years, depending on the plan.
Yes, there is a rule in the Bankruptcy Code regarding multiple bankruptcies. However, the rule doesn’t prohibit filing for multiple bankruptcies. Instead, the rule prohibits discharge of debts in multiple bankruptcies during a four year period. Normally, this would be fatal to a case because the debtor’s goal in filing for bankruptcy is to discharge debt.
However, the rule regarding multiple bankruptcies is toothless if the debtor isn’t seeking discharge. If the debtor seeks to reduce the amount of debt owed in Chapter 13 instead of discharging debt, there is no disadvantage to filing for Chapter 13 after a Chapter 7.
It depends on the state and the judge. Chapter 13 is a repayment plan. Under Chapter 13, the debtor must propose a plan to pay back his or her creditors. One of the repayment plan’s requirements is that the debtor must propose the plan in good faith. Some states and/or judges believe that Chapter 20 abuses the bankruptcy code and thus is in bad faith. Other states and/or judges have no problem with "Chapter 20" and will confirm a Chapter 13 repayment plan regardless of previous Chapter 7 filings.
Although "Chapter 20" allows debtors to make the most of the bankruptcy system, it can be extremely challenging to properly use. First, not every court will allow Chapter 20 filings. Second, not every case warrants multiple bankruptcies. Only an experienced bankruptcy attorney can advise you about the facts of your case.