1. If you currently own an HDB you can purchase a 2nd property but must be a pte property. However you have to have stayed 5 years in your HDB, after MOP(minumum occupation period).
if you do not intend to sell the HDB then you have to pay ABSD(additional buyer stamp duty of 12%).
2. if you have an HDB currently and you want to have 2 properties but do not prefer to pay ABSD then you can sell your current property and buy 2 pte properties, one under your name and the other under your spouse name. Assuming both you and your wife are working and can maintain the monthly payments. Usually we would advise one property to be a 1 bedroom that can obtain monthly passive income and the other to be a bigger one for the family stay.
3. However the above scenario is theoretical possible to achieve but its best to sit down with an salesperson to consult on the finer details and run checks for any blindspots that can be prepared.