Later debts lead to later bankruptcy
The simple answer is yes. An individual can be made bankrupt a second time even if they have not been discharged from their first bankruptcy.
As we know, any debts incurred by an individual after their date of bankruptcy is their responsibility. If they fail to meet those debts then the creditor concerned can apply to the court for an order for the person to be made bankrupt again. The fact that the individual concerned is already bankrupt is no impediment on the creditor’s application, so long as the application is based on a debt incurred after the first bankruptcy.
The implication of this second bankruptcy, given the individual is an undischarged bankrupt from the first, is dealt with under section 59 of the Bankruptcy Act. This section provides that any property of the first bankrupt estate which has not been realised or distributed to creditors by the first trustee shall immediately vest in the second trustee, in addition to any property acquired by the bankrupt after the first bankruptcy. But what are the implications for creditors of the first bankruptcy to lodge a proof of debt in the second bankruptcy.
The answer is, indirectly, they do. The trustee of the first bankrupt estate is entitled to lodge a proof of debt in the second bankruptcy for the amount of the creditors (net of any dividends paid) plus the unpaid fees and outlays of the first trustee. If there is a dividend paid by the trustee of the second bankrupt estate then the first trustee will be entitled to a dividend distribution based on the proof of debt lodged.