Yes, you must pay the deed tax for the second house at the Housing Authority, but when it comes to loans, it’s really hard to say. It depends on the specific situation. If you submit a set of loan information, the Housing Authority will also have a record of your house purchase, and the second house you buy in full will be fully deeded. If there is no filing, then your fully paid one will be one set, but the fully paid one will be filed, and the loan will be two sets.
In short, your idea is unrealistic and will it be found to have a lot to do with the regulations between your local housing management and banking departments. I can't give you the answer that best suits your local situation based on my situation here, but I still have to say that it's best not to do this.
If you can buy a second house with a one-time payment, then you must complete the loan process for the first house according to the regulations. This is performed at the most favorable interest rate. This is not the case with the full payment for the second house. What I am worried about is that I have to pay a full 3% deed tax when applying for a house.