This is not only possible, but due to the comparatively low investment threshold and the strength of the Budapest market, it is expected to be the common approach.
Yes, you can buy multiple properties, use one property for the residency program, and use the other properties for income generation.
The important factors to remember is that you must maintain ownership over a property and use it as your valid physical Budapest address.
Astons can assist investors with real estate for both pure investment and for the Hungary RBI all at the same time.